MATH 110 Sec 8-5 Lecture: Annuities – Amortization

MATH 110 Sec 8-5 Lecture: Annuities – Amortization
Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan.

Loan Amortization Formula
MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑡 is the time in years (the term) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is the # of compounding periods/yr 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is the # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is the # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Amortization is the process of paying off a loan (including interest) by making a series of regular, equal payments. The formula below is used to calculate payments on any amortized loan. This is a new formula but all of the variables are the same ones that we have used before. 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is the # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula

MATH 110 Sec 8-5 Lecture: Annuities – Amortization 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is the # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 Loan Amortization Formula Let’s illustrate the use of this formula with an example.

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be?

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000).

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 0.06 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 0.06 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12t 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =240 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1+.005) 240 =𝑅 (1+.005) 240 −1 .005 =240 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1.005) 240 =𝑅 (1.005) 240 −1 .005 =240 There was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000). 𝑃=

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1.005) 240 =𝑅 (1.005) 240 −1 .005 =240 $125000( )=𝑅 −1 .005

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1.005) 240 =𝑅 (1.005) 240 −1 .005 =240 $125000( )=𝑅 −1 .005 $125000( )=𝑅

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1.005) 240 =𝑅 (1.005) 240 −1 .005 =240 $125000( )=𝑅 −1 .005 $ =𝑅

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1.005) 240 =𝑅 (1.005) 240 −1 .005 =240 $125000( )=𝑅 −1 .005 𝑅= $ $ =𝑅

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? t= r= m=12 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(20) 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 =0.005 $ (1.005) 240 =𝑅 (1.005) 240 −1 .005 =240 $125000( )=𝑅 −1 .005 𝑅= $ $ =𝑅 𝑅=$895.54

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ How much will Ms. Rigsby pay the mortgage company over 20 years?

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ How much will Ms. Rigsby pay the mortgage company over 20 years? 𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷=𝑀𝑂𝑁𝑇𝐻𝐿𝑌 𝑃𝑀𝑇 × 12 𝑝𝑚𝑡𝑠 𝑦𝑟 ×20 𝑦𝑟𝑠

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ How much will Ms. Rigsby pay the mortgage company over 20 years? 𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷=𝑀𝑂𝑁𝑇𝐻𝐿𝑌 𝑃𝑀𝑇 × 12 𝑝𝑚𝑡𝑠 𝑦𝑟 ×20 𝑦𝑟𝑠 𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷=$895.54× 12 𝑦𝑟 ×20 𝑦𝑟𝑠

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ How much will Ms. Rigsby pay the mortgage company over 20 years? 𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷=𝑀𝑂𝑁𝑇𝐻𝐿𝑌 𝑃𝑀𝑇 × 12 𝑝𝑚𝑡𝑠 𝑦𝑟 ×20 𝑦𝑟𝑠 𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷=$895.54× 12 𝑦𝑟 ×20 𝑦𝑟𝑠 𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷=$214,929.60

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years.

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. How much interest will Ms. Rigsby pay the mortgage company?

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. How much interest will Ms. Rigsby pay the mortgage company? 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷 −𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. How much interest will Ms. Rigsby pay the mortgage company? 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷 −𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=$214,929.60−𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. How much interest will Ms. Rigsby pay the mortgage company? 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷 −𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=$214,929.60−𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷 Remember that there was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000).

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. How much interest will Ms. Rigsby pay the mortgage company? 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷 −𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=$214,929.60−$125,000.00 Remember that there was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000).

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. How much interest will Ms. Rigsby pay the mortgage company? 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=𝑇𝑂𝑇𝐴𝐿 𝑃𝐴𝐼𝐷 −𝐴𝑀𝑂𝑈𝑁𝑇 𝐵𝑂𝑅𝑅𝑂𝑊𝐸𝐷 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=$214,929.60−$125,000.00 𝑇𝑂𝑇𝐴𝐿 𝐼𝑁𝑇𝐸𝑅𝐸𝑆𝑇=$89,929.60 Remember that there was a $40,000 down payment so the present value of the loan (the amount borrowed) is $125,000 ($165,000 ‒ $40,000).

Ms. Rigsby made a $40,000 down payment on a $165,000 house and took out a 20 year mortgage at 6% compounded monthly on the balance. How much will the monthly payments be? Ms. Rigsby’s monthly payments will be $ Ms. Rigsby will pay the company $214, over 20 years. Ms. Rigsby will pay the company $89, in interest.

Let’s look at another problem.
MATH 110 Sec 8-5 Lecture: Annuities – Amortization Let’s look at another problem.

Let’s look at another problem.
MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? Let’s look at another problem.

(Note that the selling price is just the present value of an annuity.)
MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.)

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) This problem stills requires the use of the Loan Amortization Formula but here we know the amount of the loan payment (𝑅) and must find the selling price―which is just the Present Value (𝑃) of the annuity.

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 This problem stills requires the use of the Loan Amortization Formula but here we know the amount of the loan payment (𝑅) and must find the selling price―which is just the Present Value (𝑃) of the annuity.

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 This problem stills requires the use of the Loan Amortization Formula but here we know the amount of the loan payment (𝑅) and must find the selling price―which is just the Present Value (𝑃) of the annuity.

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 𝑟 𝑚 and 𝑛=𝑚𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= 0.12 𝑚 and 𝑛=𝑚𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12𝑡 ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+𝑖) 𝑛 =$200 (1+𝑖) 𝑛 −1 𝑖 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+.01) 48 =$200 (1+.01) 48 −1 .01 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 1.01= 𝑃 (1+.01) 48 =$200 (1+.01) 48 −1 .01 1.01= 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1+.01) 48 =$200 (1+.01) 48 −1 .01 1.01 1.01 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1.01) 48 =$200 (1.01) 48 −1 .01 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 (1.01) 48 =$200 (1.01) 48 −1 .01 = 𝑖= and 𝑛=48 =

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ −1 .01 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ −1 .01 = 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ 𝑖= and 𝑛=48 =

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ 𝑃 ( ) =$ 𝑖= and 𝑛=48

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ 𝑃 ( ) =$ 𝑖= and 𝑛=48 𝑃= $

MATH 110 Sec 8-5 Lecture: Annuities – Amortization m=12 Bob can afford to spend $200 each month on car payments. If he can get a 4 year auto loan at an annual rate of 12%, what is the highest selling price that can Bob afford for a car? (Note that the selling price is just the present value of an annuity.) t= r= 𝑡 is the time in years (the term) 𝑟 is the annual interest rate 𝑚 is # of compounding periods/yr 𝑅 is the amount of the periodic pmt 𝑃 is the Present Value of the annuity 𝑖= and 𝑛=12(4) ? 𝑃 (1+𝑖) 𝑛 =𝑅 (1+𝑖) 𝑛 −1 𝑖 𝑃 ( ) =$ 𝑃 ( ) =$ 𝑖= and 𝑛=48 𝑃= $ =$

Once the monthly payment on a loan has been calculated, a table called an amortization schedule can be created.

Once the monthly payment on a loan has been calculated, a table called an amortization schedule can be created. An amortization schedule provides a month-by-month breakdown of the payment, showing how much of the payment goes toward interest, how much goes toward reducing the balance owed and how much is still owed on the loan.

Let’s illustrate this with an example.
MATH 110 Sec 8-5 Lecture: Annuities – Amortization Once the monthly payment on a loan has been calculated, a table called an amortization schedule can be created. An amortization schedule provides a month-by-month breakdown of the payment, showing how much of the payment goes toward interest, how much goes toward reducing the balance owed and how much is still owed on the loan. Let’s illustrate this with an example.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ The monthly payment is fixed, so for every row, the amount in the ‘Payment’ column will be $

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ Each row represents a month so we must use 𝑖= 𝑟 𝑚 to change the 8.9% annual rate to a monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ 𝑖= 𝑟 𝑚 = Each row represents a month so we must use 𝑖= 𝑟 𝑚 to change the 8.9% annual rate to a monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ r= 𝑖= 𝑟 𝑚 = Each row represents a month so we must use 𝑖= 𝑟 𝑚 to change the 8.9% annual rate to a monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ r= 𝑖= 𝑟 𝑚 = Each row represents a month so we must use 𝑖= 𝑟 𝑚 to change the 8.9% annual rate to a monthly rate. 𝑖=

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ r= 𝑖= 𝑟 𝑚 = Each row represents a month so we must use 𝑖= 𝑟 𝑚 to change the 8.9% annual rate to a monthly rate. 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ r= 𝑖= 𝑟 𝑚 = 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ ×𝑖 So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ × So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ × So, this is the monthly rate. ?=$39.84

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ × So, this is the monthly rate. ?=$39.84

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 r= If the payment is $ and $39.84 of that goes to interest, then the amount paid on principal is $ ― $39.84 = $ 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 r= If the payment is $ and $39.84 of that goes to interest, then the amount paid on principal is $ ― $39.84 = $ − = 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 r= If the payment is $ and $39.84 of that goes to interest, then the amount paid on principal is $ ― $39.84 = $ − = 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 r= If the payment is $ and $39.84 of that goes to interest, then the amount paid on principal is $ ― $39.84 = $ 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. If $ was owed the previous month and then $ was paid on principal, then the new loan balance is $ ― $ = $ 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. If $ was owed the previous month and then $ was paid on principal, then the new loan balance is $ ― $ = $ 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 r= − 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. If $ was owed the previous month and then $ was paid on principal, then the new loan balance is $ ― $ = $ 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ r= − = 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= 𝑖= ?=$ ×𝑖 So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ × So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ ? r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ × So, this is the monthly rate. ?=$37.49

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 ?=PREV MONTH ′ S BALANCE×𝑖 𝑖= ?=$ × So, this is the monthly rate. ?=$37.49

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 r= If the payment is $ and $37.49 of that goes to interest, then the amount paid on principal is $ ― $37.49 = $ 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 r= If the payment is $ and $37.49 of that goes to interest, then the amount paid on principal is $ ― $37.49 = $ − = 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 r= If the payment is $ and $37.49 of that goes to interest, then the amount paid on principal is $ ― $37.49 = $ − = 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 r= If the payment is $ and $37.49 of that goes to interest, then the amount paid on principal is $ ― $37.49 = $ 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. If $ was owed the previous month and then $ was paid on principal, then the new loan balance is $ ― $ = $ 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. If $ was owed the previous month and then $ was paid on principal, then the new loan balance is $ ― $ = $ 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 $ r= − = 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 $ r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= So, this is the monthly rate.

Given the annual interest rate and a line of the amortization schedule for the loan (below), complete the next line of the schedule assuming monthly payments. 𝑚=12 Annual Interest Rate Payment Interest Paid Paid on Principal Balance 8.9% $357.31 $42.20 $315.11 $ $39.84 $317.47 $ $37.49 $319.82 $ r= 𝑖= 𝑟 𝑚 = The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 The interest paid in a particular month is just: 𝑃𝑅𝐸𝑉𝐼𝑂𝑈𝑆 𝑀𝑂𝑁𝑇 𝐻 ′ 𝑆 𝐵𝐴𝐿𝐴𝑁𝐶𝐸 ×𝑖 𝑖= And if we wanted to, we could continue producing more lines of this table. So, this is the monthly rate.

MATH 110 Sec 8-5 Lecture: Annuities – Amortization

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MATH 110 Sec 8-5 Lecture: Annuities – Amortization

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Presentation on theme: "MATH 110 Sec 8-5 Lecture: Annuities – Amortization"— Presentation transcript:

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