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# 7.04 Interest rates

Worksheet
Different interest rate periods
1

Find the equivalent yearly simple interest rate of the following loans. Write your answers as percentages correct to two decimal places.

a

Peter takes out a loan which earns interest at a flat rate of 0.18\% per week. Assume there are 52 weeks in a year.

b

Amelia takes out a loan which earns interest at a flat rate of 0.63\% per month.

c

Sharon takes out a loan which earns interest at a flat rate of 0.03\% per day. Assume there are 365 days in a year.

d

Carl takes out a loan which earns interest at a flat rate of 1.96\% per quarter.

2

\$5680.00 is invested at a simple interest rate of 5\% p.a. and earns \$426 in interest.

a

Calculate the number of years, taken to earn the interest correct to two decimal places.

b

Find the number of quarters taken to earn the interest.

3

The simple interest rate for an investment is 9.4\% p.a. calculated weekly. Assume there are 52 weeks in a year. Find the percentage rate used when calculating weekly interest correct to two decimal places.

4

The simple interest rate for an investment is 7.3\% p.a. calculated monthly. Find the percentage rate used when calculating monthly interest correct to two decimal places.

5

Calculate the simple interest earned on the following investments correct two decimal places. Assume that there are 52 weeks or 365 days in a year, where relevant.

a

\$5720 is invested at 10\% p.a. for 63 weeks. b \$5320 is invested at 6\% p.a. for 95 weeks.

c

\$6050 is invested at 0.7\% per quarter for 3 years. d \$9780 is invested at a rate of 5\% p.a. for 17 months.

e

\$9020 is invested at 9\% p.a. for 946 days. f \$5440 is invested at 6\% p.a. for 566 days.

6

Maria is given three investment account options by her bank, shown below:

• Option 1: Interest is earned weekly at a simple rate of 0.14\% per week.

• Option 2: Interest is earned monthly at a simple rate of 0.63\% per month.

• Option 3: Interest is earned yearly at a simple interest rate of 7.3\% p.a.

Which option should Maria go for if she wants to earn as much interest as possible?

7

Sean is offered three different loan plans when borrowing money from the bank, shown below:

• Option 1: Interest is earned daily at a simple rate of 0.02\% per day.

• Option 2: Interest is earned fortnightly at a simple rate of 0.34\% per fortnight.

• Option 3: Interest is earned quarterly at a simple interest rate of 1.98\% per quarter.

Which option should Sean go for if he wants to earn as little interest as possible?

8

Assuming that in a year, there are either 52 weeks or 365 days, where relevant. Calculate the final value of the following investments over the given time period:

a

\$5920 at 2\% p.a. for 4 years. b \$4570 at 4\% p.a. for 28 months.

c

\$9980 at 7\% p.a. for 26 weeks. d \$1430 at 8\% p.a. for 130 days.

e

\$6170 at 5\% p.a. for 6 years. f \$9060 at 4\% p.a. for 44 months.

g

\$4230 at 8\% p.a. for 32 weeks. h \$4620 at 6\% p.a. for 146 days.

9

Judy takes out a loan of \$800 to pay for an online course. Simple interest is calculated at 7\% per year, charged monthly. If she repays the loan in 6 months, how much interest does she pay in total? 10 Valentina borrowed \$5900 from the bank which was to be paid back in weekly instalments of \$65 over 2 years. Calculate the following, rounding your answers to two decimal places where necessary: a The total interest to be paid. b The interest as a percentage of the loan. c The annual interest rate. 11 Jenny takes out a loan to purchase a property. The following image depicts the change of the loan over time: a How often is Jenny making repayments? b How often is interest being added to the loan? 12 Xavier takes out a loan to purchase a property. The following graph depicts the change of the loan over time: a How often is Xavier making repayments? b How often is interest being added to the loan? Appreciation and depreciation 13 A camera valued at \$400 depreciates at a rate of \$32 per year. Calculate the amount the camera will be worth after: a One year b Two years c Ten years 14 A wrist watch valued at \$900 appreciates at a rate of \$54 per year. Calculate the amount the wristwatch will be worth after: a One year b Two years c Ten years 15 A new book depreciates in value by 6.6\% every month. The book is currently valued at \$60. Calculate the value of the book in:

a

One month

b

Two months

c

Four months

16

A car valued at \$40\,000 depreciates at a rate of \$800 per year.

a

Find the equivalent rate of simple interest depreciation.

b

Find the number of years it will take for the value of the car to depreciate to \$0. 17 A statue valued at \$12\,000 appreciates at a rate of \$240 per year. a Find the equivalent rate of simple interest appreciation. b Find the number of years it will take for the value of the statue to appreciate to three times its original value. 18 Production robots to be used in a car manufacturing plant were purchased for \$4\,455\,000. After 5 years, they depreciated to a value of \$4\,385\,000. a Find the annual depreciation using the straight-line method. b After 7 years, the robots are sold off. If they continued to depreciate at an annual rate of \$14\,000, how much can they be sold for?

19

A vintage collectors item that costs \$6000, appreciates at approximately 6.6\% p.a. After how many full years, will the value of the vintage collectors item be over \$15\,000?

20

The following graph shows the depreciation of a car's value over 4 years:

a

What is the initial value of the car?

b

By how much did the car depreciate each year?

c

After how many years will the car be worth \\$14\,400?

d

What is the value of the car after 4 years?