Examples: Investments involving compound interest calculator)

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1 SINGLE PAYMENT Examples: Investments involving compound interest calculator) (ti 83 Future value calculations 1. $1200 is invested in a Canada Savings Bond at 4.6 % compounded annually for 6 years. What is the future value of the investment, to nearest cent? 2. $ is invested in a Canada Savings Bond at 5.8 % compounded quarterly for 6 years. What is the future value of the investment, to nearest cent? Present value calculations (Principal) 3. Max would like to have $ in an investment when he retires in 20 years. How much money should be invested now, at 8.5 % compounded annually? 4. Erika would like to have $ in an investment when she retires in 10 years. How much money should be invested now, at 6.2 % compounded quarterly? 1

2 Interest calculations 5. Jarrod is investing $8000 into a savings bond. He wants to have $ in his investment in 10 years. What interest rate, compounded monthly, will result in a future value of $15 000? Round to one decimal place. 6. Jarrod is investing $6 000 into a savings bond. He wants to have $8 500 in his investment in 5 years. What interest rate, compounded annually, will result in a future value of $8 500? Round to one decimal place. RULE of 72 2

3 Time calculations NOTE: Be careful when figuring out time, n represents the number of compounding periods not years. Always convert n to years when doing on graphing calculator 7. Parker invests $8000 at 6 % compounded annually when will the investment be worth double? Estimate with rule of 72 and then with Ti 83 calculator 8. Chris invests $5000 at 2.4 % compounded quarterly when will the investment be worth double? Estimate with rule of 72 and then with Ti 83 calculator 9. Simon invests $8000 at 3.6 % compounded semi annually when will the investment be worth double? Estimate with rule of 72 and then with Ti 83 calculator Section 1.5: Investments Involving Regular Payments For an investment that involves a series of equal payments made at regular intervals, the future value is the sum of all the regular payments plus the accumulated interest. where A is the amount, or future value of the investment, R is the regular payment, i is the interest rate per compounding period, expressed as a decimal, and n is the number of compounding periods. (Basically treating each payment as a single investment and then adding up al the future values of each payment. Each payment earns interest over a different amount of time. Payments made earlier will make more interest then later payments. ) The future value of a single deposit has a greater future value than a series of regular payments of the same total amount. Small deposits over a long term can have a greater future value than large deposits over a short term because there is more time for compound interest to be earned. Note: all examples involve payments made at the END of each payment period. 3

4 1. Darva is saving for a trip to Australia in 3 years. She deposits $500 into her savings account at the end of each 6 month period. The account earns 4 % compounded semi annually. a) How much money will be in the account at the end of 3 years? b) What is the interest earned? c) If the same principal was invested as a single payment investment. What would be the future value of the investment? The future value of a single deposit has a greater future value than a series of regular payments of the same total amount. Ex. 2 Kendra deposits $100 into an investment account at the end of each year. The account earns 9 %interest compounded annually. How much will be in the account at the end of 3 years? How much of this money will earned interest? 4

5 Your Turn: Warm up Investments involving regular payments Kayla deposits $160 into an investment account at the end of each half year. The account earns 6.2 %interest compounded semi annually. How much will be in the account at the end of 3 years? How much of this money will earned interest? $160 $160 $160 $160 $160 $ (1.031) 0 = (1.031) 1 = (1.031) 2 = (1.031) 3 = (1.031) 4 = (1.031) 5 = Sophia deposits $750 into her savings account t the end of each 3 month period. The account earns 2.8%, compounded quarterly. USE Ti 83 a) How much will be in the account at the end of 3 years? To determine the future value of her investments, you would need to do 12 separate calculations and then add them together. (There are 4 calculations per year for 3 years!) UGHHHH... 5

6 Thankfully, we will solve problems like this using the financial application on a graphing calculator. 3. Sophia deposits $750 into her savings account t the end of each 3 month period. The account earns 2.8%, compounded quarterly. USE Ti 83 a) How much will be in the account at the end of 3 years? b) How much of this money will earned interest? 6

7 Example: Compare a regular payment investment with a single payment investment 4. Adam made $200 payment at the end of each year into an investment that earned 5%, compounded annually. Blake made a single investment at 5 % compounded annually. At the end of 5 years, their future values were equal. a) What was their future value? b) What principle amount did Blake invest 5 years ago? c) Who earned more interest and why? With regular payment investments, only the 1st payment earns interest for entire term. Each payment after that earns less and less interest. Ex (4) Predict which investment will earn more interest. Explain and then verify your prediction. A. $8000 invested at 5% compounded annually, for 8 years B. $1000 invested every year at 5% compounded annually, for 8 years Prediction Option A Option B 7

8 1. Mike is saving up to buy a washer and dryer in 2 years. He plans to deposit the same amount at the end of each month into an account that pays 1.9% compounded monthly. What regular payments must he make at the end of each month to meet his goal of $1300? What interest will he earn? 2. Sally wants to have $ in 20 years. She invests in a trust account that earns a fixed rate of interest of 10.2 % compounded annually. What regular payments must she make at the end of each year to meet her goal of $30 000? What interest will he earn? 8

9 3. Jeremy deposits $750 into an investment account at the end of every 3 months. Interest is compounded quarterly, the term is 3 years, and the future value is $ What annual rate of interest does Jeremy s investment earn to nearest tenths place? 4. On Lance s 20 th birthday, he started making regular $1000 payments into an investment account at the end of every 6 months. He wants to save for a down payment on a home. His investment earns 3.5% compounded semi annually. At what age will he have more than $18000 in his investment? PMT: END What payments would Lance have to make if he wanted exactly $18000 in 8 years? PMT: END 9

10 5. When June turned 18, she stated that she would like to be a millionaire when she retired at age 50. To reach this goal, she decided to invest $3000 quarterly for the next 32 years. If her investment paid 6% per year compounded quarterly, will she reach her goal? If so, by how much will she exceed it? o 10