Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Chapter 14 of

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Calculate Learning Objectives …the principal balance after any payment using both the Prospective Method and the Retrospective Method After completing this chapter, you will be able to: … the principal and interest components of any payment And… … the final loan payment when it differs from the others LO 1. LO 2. LO 3.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Learning Objectives Calculate LO 4. LO 5. … mortgage loan balances and amortization periods to reflect prepayments of principal … mortgage payments for the initial loan and its renewals

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© A $20,000 mortgage loan at 9% compounded monthly requires monthly payments during its 20-year amortization period. (1) Calculate the monthly payment. (2) Using the monthly payment from part (1), calculate the PV of all payments. (3) Why does the answer in (2) differ from $20,000? PMT = n =12* 20 = 240PV = $20000FV = & & 3. LO 1.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© (2) Using the monthly payment from part (1), calculate the PV of all payments. (3) Why does the answer in (2) differ from $20,000? n =12*20 = 240PV = ?FV = 0PMT = PV = 20, The difference of $ is due to rounding the monthly payment to the nearest cent!

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Calculate the exact balance after 5 years assuming the final payment will be adjusted for the effect of rounding the regular payment. A $20,000 mortgage loan at 9% compounded monthly requires monthly payments during its 20-year amortization period. Calculate the exact n for monthly payments of $ to repay a $20,000 loan N =

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Calculate the exact balance after 5 years assuming the final payment will be adjusted for the effect of rounding the regular payment. A $20,000 mortgage loan at 9% compounded monthly requires monthly payments during its 20-year amortization period. After 5 years, – 60 = payments remain. Therefore, balance (after 5 years) = PV of payments of $ N = N = P/V = 17,741.05

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© An Original Loan = Consider that… The PV of ALL of the Payments (discounted at the contractual rate of interest on the loan) Also, that… A Balance =The PV of the remaining Payments (discounted at the contractual rate of interest on the loan) Then…

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© …this can be expressed as …the Statement of Economic Equivalence (Original Loan) Focal Date… PV of first x Payments PV of the Balance just after the xth Payment For a focal date of the original date of the loan,

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© of the xth payment, the Statement of Economic Equivalence becomes… Retrospective Method for Loan Balances Retrospective Suppose we locate theFocal Date… Balance This is now rearranged to isolate the “Balance” Balance FV of the Original Loan FV of the Payments already made FV of the Original Loan FV of the Payments already made

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Retrospective Method for Loan Balances Retrospective … is based on PAYMENTS ALREADY MADE!` Prospective Method for Loan Balances … is based on PAYMENTS YET to be MADE!` Application

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Calculate the exact balance after 5 years. A $20,000 mortgage loan at 9% compounded monthly requires monthly payments of $ during its 20-year amortization period. Solve using… Retrospective Method Prospective Method Then compare…

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Retrospective Method for Loan Balances Calculate the exact balance after 5 years. A $20,000 mortgage loan at 9% compounded monthly requires monthly payments of $ during its 20-year amortization period. Balance = FV of $20,000 – FV of first 60 payments , * 5 Years FV= 17,741.05

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Prospective Method for Loan Balances Calculate the exact balance after 5 years. A $20,000 mortgage loan at 9% compounded monthly requires monthly payments of $ during its 20-year amortization period. 12* 20 Years = 240 Total payments = PV= 17, made = 180 remaining Balance = PV of remaining 180 payments

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Difference ($0.83) is because the Prospective Method assumes that the final payment is the same as all the others. The Retrospective Method is based on payments already made. FV= 17, Retrospective Method for Loan Balances PV= 17, Prospective Method for Loan Balances Comparison of Methods

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Final Payment = (1+i) * (Balance after 2 nd to last payment) Balance after 239 payments = FV of $20,000 after 239 months – FV of 239 payments FV= ,000 Final Payment = (1+0.09/12) * = $ Calculate the size of the final payment. A $20,000 mortgage loan at 9% compounded monthly requires monthly payments of $ during its 20-year amortization period. LO 2.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Meditech Laboratories borrowed $28,000 at 10%, compounded quarterly, to purchase new testing equipment. Payments of $1,500 are made every 3 months. A. Calculate the balance after the 10th payment. B. Calculate the final payment. Meditech Laboratories borrowed $28,000 at 10%, compounded quarterly, to purchase new testing equipment. Payments of $1,500 are made every 3 months. A. Calculate the balance after the 10th payment. B. Calculate the final payment. Balance after 10 payments = FV of $28,000 after 10 quarters – FV of 10 payments FV= - 19, ,000 A.A. B.B Needed Balance after 10 payments

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Meditech Laboratories borrowed $28,000 at 10%, compounded quarterly, to purchase new testing equipment. Payments of $1,500 are made every 3 months. A.Calculate the balance after the 10th payment. Meditech Laboratories borrowed $28,000 at 10%, compounded quarterly, to purchase new testing equipment. Payments of $1,500 are made every 3 months. A.Calculate the balance after the 10th payment. …the number of payments 1. Calculate 0 N = FV = …the balance after the 2 nd to last payment 2. Calculate 3. B. Calculate the final payment.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© …the final payment 3. Calculate Meditech Laboratories borrowed $28,000 at 10%, compounded quarterly, to purchase new testing equipment. Payments of $1,500 are made every 3 months. A. Calculate the balance after the 10th payment. B. Calculate the final payment. Meditech Laboratories borrowed $28,000 at 10%, compounded quarterly, to purchase new testing equipment. Payments of $1,500 are made every 3 months. A. Calculate the balance after the 10th payment. B. Calculate the final payment. Final Payment = (1+0.10/4) * = $690.63

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate the interest and principal components of the 29th payment. B. How much interest will be paid in the second year of the loan? LO 3.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate the interest and principal components of the 29th payment. B. How much interest will be paid in the second year of the loan? A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate the interest and principal components of the 29th payment. B. How much interest will be paid in the second year of the loan? First: … find the size of the monthly payment PV =n =i = (4) = / PMT =

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate the interest and principal components of the 29th payment. A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. A. Calculate the interest and principal components of the 29th payment. A.A. First: … find the balance after the 28 payments 28 PMT = FV = Interest Component of Payment 29 = 0.105/12* = $38.89 = i * Balance after 28th payment Principal Component = PMT – Interest Component = $ $38.89 = $204.34

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. B. How much interest will be paid in the second year of the loan? A $9,500 personal loan at 10.5% compounded monthly is to be repaid over a 4-year term by equal monthly payments. B. How much interest will be paid in the second year of the loan? First:… find the balance after 1 Year, and the balance after 2 Years 12 FV = Total Principal paid in year 2 = $7, $5, = $2, FV = Total Interest paid in year 2 = 12($243.23) - $2, = $ Balance after 1 year Balance after 2 years B.B.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© … is a loan secured by some physical property

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© MORTGAGE APPLICATION Mortgage Loans …Basic Concepts and Definitions …the borrower is called the mortgagor …the lender is called the mortgagee Borrower Lender

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© MORTGAGE APPLICATION Mortgage Loans …Basic Concepts and Definitions Face Value of mortgage = original principal amount Term …From … date on which loan advanced To … date on which the remaining Principal Balance is due and payable …most common periods are 20 and 25 years. Interest Rate …usually a lender will commit to a fixed interest rate for only a shorter period or term (6 months to 7 years)

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© MORTGAGE APPLICATION A Mortgage Loan at 8.5% compounded semiannually with a 25-year amortization period Graphic Illustrations

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© YearsInterest % The Composition of Mortgage Payments during a 25-year Amortization Principal Component Approximately 40% Approximately 60% Year 14 Interest Component

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Years Principal Balance $ 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90, ,000 Mortgages Declining Balance during a 25-year Amortization Principal declines slower in earlier years

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson©

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© MORTGAGE APPLICATION …need to satisfy all 3 of the following Ratios… Loan-to-Value Ratio (LVR) Gross Debt Service Ratio (GDS) Total Debt Service Ratio (TDS)

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© MORTGAGE APPLICATION Loan-to-Value Ratio (LVR) Gross Debt Service Ratio (GDS) Total Debt Service Ratio (TDS) Principal Amount of Loan Lending Value of Property x 100%  75% Total monthly payments for Mortgage, Property taxes, and Heat Gross Monthly Income x 100%  32% Total monthly payments for Mortgage, Property taxes, Heat and Other Debts Gross Monthly Income x 100%  40%

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© You have saved $35,000 for the down payment on a home. You want to know the maximum conventional mortgage loan for which you can qualify in order to determine the highest price you can pay for a home. What maximum monthly mortgage payment do the GDS and TDS ratios permit? … gross monthly income is $3,200 … 18 payments of $300 per month remaining on a car loan … property taxes of $150 per month and heating costs of $100 per month … the bank has upper limits of 32% for the GDS Ratio and 40% for the TDS Ratio … gross monthly income is $3,200 … 18 payments of $300 per month remaining on a car loan … property taxes of $150 per month and heating costs of $100 per month … the bank has upper limits of 32% for the GDS Ratio and 40% for the TDS Ratio Personal Data

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Gross Debt Service Ratio (GDS) Total monthly payments for Mortgage, Property taxes, and Heat Gross Monthly Income x 100%  32% Maximum Mortgage payment $3,200 = 32% Maximum Mortgage payment =.32(3200) = $774

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Total Debt Service Ratio (TDS) Total monthly payments for Mortgage, Property taxes, Heat and Other Debts Gross Monthly Income x 100%  40% Maximum mortgage payment $3,200 = 40% Maximum Mortgage payment =.40(3200) = $730

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© What is the maximum mortgage for which you qualify? Use a 25-year amortization and an interest rate of 8% compounded semiannually for a five-year term P/Y = 12 C/Y = 2 0P/V= 95, Maximum Mortgage

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Loan-to-Value Ratio (LVR) x Principal Amount of Loan Lending Value of Property 100%  75% $95, 600 Minimum house value = 75% Minimum house value = $95, % = $127, Based on a $35,00 down payment and the maximum loan possible, what is the highest price you can pay for a home?

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© At this price, the minimum down payment is: $127,531– $95,648= $ 31,883 … the maximum price you can afford to pay for a home is… $35,000 – 31,882 (Minimum down payment ) = over DP $35,000 – 31,882 (Minimum down payment ) = over DP Based on a $35,00 down payment and the maximum loan possible, what is the highest price you can pay for a home? + $127, 531 = $130,649$3,118

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© MORTGAGE APPLICATION Common Prepayment Privileges Penalties &

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Partially Open Fully Open Common Prepayment Privileges Penalties & & No restrictions or penalties on extra payments by the borrower! Limited penalty-free prepayment Lump or Balloon Payments 10% or 15% of the original amount Increasing the Regular Payment…permanently Once a year by 10% or 15% “Double-Up” Pay twice the amount for any monthly payment Closed No prepayment without a penalty

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Financial Penalties Common Prepayment Privileges Penalties & & Contract provides for a financial penalty on any prepayment not specifically permitted The most common prepayment penalty is the greater of: Three months’ interest on the amount prepaid, or Three months’ interest on the amount prepaid, or The lender’s reduction in interest revenue from the prepaid amount (over the remainder of the mortgage’s term) Example

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© The interest rate for the first 5-year term of a $100,000 mortgage loan is 7.5% compounded semiannually. The mortgage requires monthly payments over a 25 year amortization period. The mortgage contract gives the borrower the right to prepay up to 10% of the original mortgage loan, once a year, without interest penalty. Suppose that, at the end of the second year of the mortgage, the borrower makes a prepayment of $10,000. a)How much will the amortization period be shortened? b)What will be the principal balance at the end of the five-year term? a)How much will the amortization period be shortened? b)What will be the principal balance at the end of the five-year term? Solving Steps LO 4. LO 5.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© …the payments based on a 25-year amortization …the balance after 24 payments - Reduce this balance by $10,000 …the number of monthly payments needed to pay off this new balance …the reduction in the original 25-year amortization period Calculate

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© , PMT= PV =n =i = c = 100,00025*12 = /22/12 2 …the payments based on a 25-year amortization 1. Calculate monthly payment 2. 3.

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© FV= -97, ,000 87, …the balance after 24 payments 2. Calculate - Reduce this balance by $10, balance after 24 payments balance after the prepayment

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© , …with the prepayment: = 239 Total payments Therefore, = 61 months saved... i.e. 5 yrs 1 month …the number of monthly payments needed to pay off this new balance 4. Calculate…the reduction in the original 25-year amortization period 5. Calculate N= more payments to pay off the mortgage

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© Click On: Student Centre Select: Interactive Mortgage Payoff Chart …online Interactive Mortgage Payoff Chart …online Click On: -or- Select: 4 th Edition Click On:

Amortization of Loans Amortization of Loans 3 3 McGraw-Hill Ryerson© This completes Chapter 14