Calculate 10% of each number and then add it to the number MCR 3UI Unit 7 – Day 1 Calculate 10% of each number and then add it to the number a) $100 b) $250 Calculate 10% of answer and then add it to the answer a) b) Repeat the process 2 more times. a) b) Is there a faster way to calculate the final answers you got?

Monday Tuesday Wednesday Thursday Friday In-Class Assignment Dec 17 Compound Interest And Present Value Dec 18 Annuities Dec 19 More Investments Dec 20 In-Class Assignment Dec 21 Finish outstanding work. (HW for week due) Christmas Break Jan 7 Exponential Functions and Apps Jan 8 Jan 9 Jan 10 Jan 11 Jan 14 Jan 15 Jan 16 Jan 17 Jan 18 Unit 7 Test (Material from after Christmas only) Jan 21 Exam Review Jan 22 Jan 23 Jan 24 Period 1 Exam Jan 25 Period 2 Exam Jan 28 Period 3 Exam Jan 29 MATH EXAM !! Jan 30 Jan 31 Feb 1

Unit 7 – Day 1: Compound Interest and Present Value Explain what compound interest is. Determine the future value of an investment/loan and the amount of interest earned. Determine the present value of an investment/loan and the amount of interest earned.

For the right to use your money they pay you. Explain what compound interest is. If you invest money in a bank (or many other types of investments) then the bank can use your money. For the right to use your money they pay you. They usually pay you a percentage of the money you invest. This payment is known as interest. The money you originally invested in known as the principal. If you borrow money from a bank or do not pay for something right away then you must (usually) pay extra money for this right/ability. This charge is also known as interest.

If you invest $100 and get 10% compound interest ….. Explain what compound interest is. If you invest $100 and get 10% compound interest ….. 100 1+0.10 1 = 110.00 100 1+0.10 2 = 121.00 100 1+0.10 3 = 133.10 100 1+0.10 4 = 146.41 100 1+0.10 10 = 259.37 100 1+0.10 20 = 672.75 If you invest $100 and get 10% not compound interest ….. With compound interest your money grows faster because you get interest on the interest.

Example 1: Number of compounding periods and interest per period. Explain what compound interest is. Example 1: Number of compounding periods and interest per period. Determine the number of compounding periods and the interest per period. a) 5%/a compounded annually for 10 years b) 8%/a compounded semi-annually for 7 years c) 5.5%/a compounded quarterly for 30 months d) 9.4%/a compounded monthly for 26 weeks

Example 2: Determining the future value and the amount of interest Determine the future value of an investment/loan and the amount of interest earned. Example 2: Determining the future value and the amount of interest Use the formula 𝐴=𝑃 1+𝑖 𝑛 to determine the future value and the amount of interest. a) You bought a new TV which cost $1000. You were given the option to defer your payment for 2 years with interest of 6%/a compounded monthly. How much will you owe in 2 years? What amount of interest will you be charged? b) Suppose you made a down payment of $400. How much less interest would you be charged? c) Suppose interest was 7%/a compounded quarterly and you only waited 18 months to pay. (No down payment) How much would you owe?

Example 3: Determining the present value and the amount of interest Determine the present value of an investment/loan and the amount of interest earned. Example 3: Determining the present value and the amount of interest Use the formula 𝑃=𝐴 1+𝑖 −𝑛 to determine the present value and the amount of interest. a) You want to have $15,000 saved for your first year of school. How much would you need to invest now if you want to go to school in 3 years and interest is 4%/a compounded annually. How much interest would you earn? b) Suppose interest was 4%/a compounded monthly. Would you earn more or less interest? How much more/less? c) Suppose the money had been invested when you were 5 years old and you planned to go to school at the age of 18. If interest was 4%/a compounded annually how money would you have needed to invest? How much interest would you have earned?

𝐴=𝑃 1+𝑖 𝑛 𝑃=𝐴 1+𝑖 −𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 8. Find the balance of the investment if $1000 is compounded annually, at 5%/a for (a) 10 years (b) 20 years (c) 30 years -------------------------------------------------------------------------------------------------------------------- 10. On the day his son is born, Mike wishes to invest a single sum of money that will grow to $10 000 when his son turns 21. If Mike invests the money at 4%/a compounded semiannually, how much must he invest today? start 10 years 𝐴=𝑃 1+𝑖 𝑛 $1000 ??? born 21 years 𝑃=𝐴 1+𝑖 −𝑛 ??? $10000

𝑃=𝐴 1+𝑖 −𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 13. Barry bought a boat two years ago and at that time paid a down payment of $10 000 cash. Today he must make a second and final payment of $7500, which includes the interest charge on the balance owing. Barry financed this purchase at 6.2%, compounded semiannually. Determine the purchase price of the boat. 2 years ago now 𝑃=𝐴 1+𝑖 −𝑛 Then find total purchase price $10000 + ??? $7500

𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 14. Tiffany deposits $9000 in an account that pays 10%/a compounded quarterly. After three years, the interest rate changes to 9%/a compounded semiannually. Calculate the value of her investment two years after this change. start 3 years 5 years (2 more) 10% quarterly 9% semiannually $9000 ??? ??? 𝐴=𝑃 1+𝑖 𝑛 twice

𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 15. Exactly six months ago, Lee borrowed $2000 at 9% compounded semiannually. Today he paid $800, which included principal and interest. What must he pay to close the debt at the end of the year (six months from now) 6 months ago now 6 months from now $2000 ??? - 800 ??? 𝐴=𝑃 1+𝑖 𝑛 twice

𝑃=𝐴 1+𝑖 −𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 16. Today Sigrid has $7424.83 in her bank account. For the last two years, her account has paid 6%/a, compounded monthly. Before then, her account paid 6%/a, compounded semiannually, for four years. If she made only one deposit six years ago, determine the original principal. 6 years ago 2 years ago Today 6% semi annually 6% monthly ??? ??? 7424.83 𝑃=𝐴 1+𝑖 −𝑛 twice

𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 19. Bernie deposited $4000 into the “Accumulator Account” at his bank. During the first year, the account pays 4%/a, compounded quarterly. As an incentive to the bank’s customers, this account’s interest rate in increased by 0.2% each year. Calculate the balance in Bernie’s account after three years. now 1 year 2 years 3 years 4% quarterly 4.2% quarterly 4.4% quarterly 4000 ??? ??? ??? 𝐴=𝑃 1+𝑖 𝑛 three times

𝐴=𝑃 1+𝑖 𝑛 Which formula to use? Today’s HW: pg 71 , #8, 10, 13 – 16, 19, 20 20. On the day Sarah was born, her parents deposited $500 in a savings account that earns 4.8%/a, compounded monthly. They deposited the same amount on her 5th, 10th, and 15th birthdays. Determine the balance in the account on Sarah’s 18th birthday. birth 5 years 10 years 15 years 18 years 500 ???+500 ???+ 500 ???+500 ??? 𝐴=𝑃 1+𝑖 𝑛 four times