 6.02 Compound interest using the financial application

Worksheet
Final value
1

Find the future value of the following investments:

a

\$3000 is invested at an interest rate of 5\% p.a. compounded annually for 17 years. b \$3000 is invested at an interest rate of 4\% p.a. compounded quarterly for 17 years.

c

\$6000 is invested at an interest rate of 2.5\% p.a. compounded monthly for 3.5 years. d \$10\,000 is invested at an interest rate of 2.7\% p.a. compounded monthly for 18 months.

e

\$15\,000 is invested with at an interest rate of 0.7\% per month compounded monthly for 23 months. 2 Find the future value of the following loans: a \$13\,000 is borrowed at an interest rate of 2.5\% p.a. compounded semi-annually for 3.5 years.

b

\$2000 is borrowed at an interest rate of 12\% p.a. compounded monthly for 2 years. c \$5000 is borrowed at an interest rate of 3.5\% p.a. compounded daily for 4 years.

d

\$500 is borrowed at an interest rate of 10.7\% p.a. compounded daily for 10 weeks. e \$2000 is borrowed at an interest rate of 1.6\% per quarter compounded quarterly for 4 years.

3

Ryan borrows \$4000 at a rate of 5.5\% p.a. compounded weekly. Assuming he makes no repayments, find how much he owes after 1 year. 4 Skye takes out a car loan of \$32\,000 at an interest rate of 0.01\% per day compounded monthly. If she makes no repayment, find how much she owes after 5 years.

5

\$218 is invested at 2\% p.a. compounded annually for 5 years. After this time the principal plus interest is reinvested at 3\% p.a. compounded annually for 2 more years. Use the finance facility on your calculator to find the final value of the investment. Interest 6 \$2000 is invested at an interest rate of 4\% p.a. compounded quarterly.

a

Find the value of the investment after 15 years.

b

Find the amount of interest earned over the 15 years.

7

\$10\,000 is invested at an interest rate of 2.5\% p.a. compounded monthly. Find the amount of interest that is added to the account over 24 months. 8 \$24\,000 is deposited in a savings account which attracts interest at 1.3\% p.a. compounded daily. Find the amount of interest that is earned over 9 years. Assume there are 365 days in a year.

9

\$12\,000 is invested at an interest rate of 0.4\% per month compounded monthly. Find the amount of interest that is earned over 4.5 years. 10 \$5000 is borrowed at an interest rate of 12\% p.a. compounded monthly:

a

Find the amount owed after 3 years.

b

Find the amount of interest accrued over the 3 years.

11

Nadia borrows \$12\,000 at an interest rate of 3.5\% p.a. compounded weekly. If she makes no repayments, find the amount of interest that is owed after 3 years. Principal 12 Maximilian wants to have \$1500 at the end of 5 years. The bank offers 7.8\% p.a. compounded annually. Use the finance facility on your calculator to calculate how much he should invest now.

13

Katrina has her property investment currently valued at \$750\,000 and she knows that its value increased at a rate of 10\% p.a. compounded annually for the last 20 years. Find the value of her investment at the beginning of the 20 years. 14 A savings account has a balance of \$25\,500 after 10 years of interest at 1.6\% p.a. compounded quarterly. Find the initial deposit.

15

Jack is aiming to save \$35\,000 after 10 years of investing at an interest rate of 0.1\% per week compounded monthly. Find the amount he needs to deposit as a principal. Assume there are 52 weeks in a year. 16 Harry expects to receive a Christmas bonus of \$7000 in 6 months time. His credit card incurs interest at 14\% p.a. compounded weekly with no interest free period. What is the most he can spend now using his credit card and still be able to pay it off using his Christmas bonus?

Interest rate
17

A \$2000 investment grows to \$4000 over 2 years accumulating interest which is being compounded monthly. Calculate the interest rate per annum which is being applied. Give your answer as a percentage to two decimal places.

18

What interest rate per annum would be required to double an investment of \$1000 in 2 years if the interest is compounded daily? Assume there are 365 days in a year. Give your answer as a percentage to two decimal places. 19 What interest rate per annum would be required to double an investment of \$P in 4 years time, if the interest is compounded quarterly? Give your answer as a percentage to two decimal places.

Investment period
20

\$1000 is placed in a term deposit with a rate of 5\% p.a. compounded annually. How many whole years will it take for the balance to increase in value to at least \$1500?

21

Nadia invests \$1200 in a term deposit with a rate of 2.3\% p.a. compounded monthly. How many whole months will it take for the investment to increase in value to at least \$1500?

22

Neil invests \$900 in a term deposit with a rate of 2.3\% p.a. compounded daily. How many years will it take for the investment to at least double in value? Assume there are 365 days in a year. 23 How many whole years will it take an investment of \$P to at least double in value at an interest 4.2\% p.a. is compounded quarterly?

24

Vanessa borrows \$25\,000 at an interest rate of 4.3\% p.a. compounded annually in order to pay for her university degree. If she continues into postgraduate study and therefore makes no repayments, how many whole years will it take for her debt to reach at least \$40\,000?

Applications
25

Use the finance facility on your calculator to find the value of a \$1460 collection of brand new shoes after 6 years when the annual inflation rate is 6\%? 26 The value of land is expected to grow by 6\% each year for the next 4 years. If it currently costs \$610 per square metre, use the finance facility on your calculator to calculate how much it will cost at the end of 4 years.

27

Use the finance facility on your calculator to find the value of a stamp collection, currently valued at \$4770, after 6 years if its rate of appreciation is 10\% p.a.? 28 Due to dwindling supplies of oil, oil prices are expected to appreciate by 7.1\% p.a. If the current price of oil is \$76 per barrel, use the finance facility on your calculator to find the expected price of a barrel in 29 years time.

29

For an inflation rate of 6.1\% per annum, find the expected value of a \$250 basket of groceries 9 years from now, using the finance facility of your calculator. 30 Laura has a choice between a high-risk investment which attracts interest at 10\% p.a. compounded annually, and a low-risk investment at 5\% p.a. compounded annually. She has \$50\,000 to invest and her goal is to grow it to \$60\,000 within 3 years. Which of the investments would allow her to reach her goal? 31 In 2001, the price of a bottle of orange juice was \$2.60. Use the finance facility of your calculator to find the price of a bottle of orange juice in 2007 if the inflation rate was 11\% per annum.