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10.03 Interest and loans

Worksheet
Simple interest
1

Calculate the simple interest on the following:

a

An investment of \$8840 at 6\% p.a. for 2 years.

b

A 2-year loan of \$3000 at 17\%. p.a.

c

A loan of \$8000 at 8\% p.a. for 6 years.

d

An investment of \$2540 at 9\% p.a. for 2 years.

e

An investment of \$7000 at 7.2\% for 9 years.

2

For a simple interest rate of 10\% p.a., calculate the number of years needed for an interest of \$1149.60 to be earned on an investment of \$2874.

3

Find the annual interest rate as a percentage to one decimal place for the following scenarios:

a

The simple interest on an investment of \$2650 over 3 years is \$787.05.

b

The simple interest on a loan of \$2830 over 10 years is \$2603.60.

c

The simple interest on a loan of \$6600 over 33 months is \$1252.35.

d

The simple interest on an investment of \$3600 over 2 years is \$504.00.

e

The simple interest on a loan of \$7550 over 9 years is \$6523.20.

4

Find the total amount to be paid on a 4-year, \$90\,000 loan at 12\% p.a. flat interest.

5

The graph shows the amount of simple interest charged each year by a particular bank, on some 9-year loan.

a

Find the total amount of simple interest charged on a loan of \$4000.

b

Calculate the simple interest rate per annum charged by the bank on these 9-year loans. Give your answer as a percentage.

1000
2000
3000
4000
\text{Principal}
50
100
150
200
250
300
\text{Interest}
6

Homer borrowed \$7600 from a bank at a simple interest rate of 4.5\% for one year.

a

How much interest will Homer need to pay after 1 year?

b

Calculate the total amount Homer will have to repay the bank at the end of 1 year.

7

\$906 is invested at 5\% p.a simple interest. Dave wants to know the number of years it will take the investment to grow to \$1132.50.

a

Calculate the interest that will be earned on the investment.

b

Calculate the number of years it will take the investment to grow to \$1132.50.

8

If \$4948 is invested at 8\% p.a. simple interest for 7 years, find the simple interest rate that would earn the same amount of interest in only 5 years. Give your answer as a percentage rounded to two decimal places.

9

For a simple interest rate of 6\% p.a., calculate the number of years needed for an interest of \$1174.20 to be earned on the investment \$1957. Give your answer as a whole number of years.

10

\$552 is invested at 5\% p.a simple interest. Dave wants to know the number of years it will take the investment to grow to \$828.00.

a

Calculate the interest that will be earned on the investment.

b

Calculate the number of years it will take the investment to grow to \$828.00

11

For a simple interest rate of 8\% p.a., calculate the number of months that \$63\,790 needs to be invested to earn \$7654.80 in interest.

a

Find the number of years taken to earn the interest.

b

Hence, find the number of months taken to earn the interest. Give your answer to the nearest month.

12

For how many years does \$7050 need to be invested for it to grow to \$7950, if simple interest is paid at 7\% p.a.? Round your answer correct to two decimal places.

13

For his investment into government bonds, Buzz was paid simple interest of 9\% p.a. Calculate the size of Buzz's initial investment if he earned \$294.12 interest after 2 years.

14

Luke's investment of \$3000 earned simple interest of 4\% p.a. for the first 8 years and 2\% p.a. for the next 5 years. Calculate the total amount of interest earned.

15

Dave and Emily are looking to invest \$11600 and \$18300 respectively for 6 years. The simple interest rate applied is determined by the following table:

PrincipalRate p.a.
\text{Between } \$4800\text{ and } \$14\,8004\%
\text{Between } \$14\,800\text{ and } \$24\,8005\%
\text{Greater than } \$24\,8006\%
a

How much interest will Dave earn on his investment?

b

How much interest will Emily earn on her investment?

c

How much will they earn if they invest their principals together?

d

How much more interest will they earn by combining their principals?

16

If \$2196 is invested at 2\% p.a. simple interest for 8 years, what simple interest rate would earn the same amount of interest in only 5 years? Give your answer as a percentage rounded to two decimal places.

Loan repayments
17

Katrina takes out a loan to purchase a surround sound system. She makes 19 equal loan repayments. The total loan amount paid is \$95\,000. Find the value of each repayment.

18

Lisa takes out a loan to purchase a small boat. She pays it back in equal monthly repayments over 6 years. The total loan amount paid back is \$55\,800. Calculate the amount of each repayment.

19

Iain takes out a loan to purchase a jetski. He makes 15 equal loan repayments of \$5239. Calculate the total amount paid back on the loan.

20

Tara takes out a car loan of \$6000 at a simple interest rate of 8\% p.a. She plans to repay the loan over 2 years through regular monthly repayments.

a

Calculate the total interest that Tara will accrue over the duration of the repayment.

b

Hence, calculate the value of each repayment of the loan.

21

A borrower received a loan of \$5500 which was to be repaid in monthly installments of \$269 over 3 years.

a

Calculate the total repayments.

b

Calculate the total interest to be paid.

c

Calculate the flat rate of interest per annum as a percentage to two decimal places.

22

Sally made loan repayments totalling to \$8960 on a loan of \$8000 over 6 years.

a

Calculate the total simple interest charged on the loan.

b

Calculate the annual simple interest rate as a percentage value.

23

Kathrine took out a loan of \$5600 which was to be repaid in monthly instalments of \$261 over 2 years. Calculate the following, rounding your answers to two decimal places where necessary:

a

The total repayments.

b

The total interest to be paid.

c

The interest as a percentage of the loan.

d

The effective annual interest rate.

24

Susana takes out a car loan. The last few months of Susana's repayments are shown below:

MonthOpening BalanceInterestRepaymentClosing Balance
69868.484.34250622.82
70622.823.11250375.93
71375.931.88250127.81
a

Calculate the monthly interest rate charged on this loan to one decimal place.

b

Complete the next row of the table for month 72, rounding your answers to two decimal places.

c

How many years did it take for her to pay off the loan?

d

Calculate her total repayments.

e

If her loan was for \$15\,000, calculate the total interest paid on the loan.

25

Mr and Mrs Maximilian have a mortgage. The final months of their repayments are shown below:

MonthOpening BalanceInterestRepaymentClosing Balance
14626\,452.84198.40500021\,651.24
14721\,651.24162.38500016\,813.62
14816\,813.62126.10500011\,939.72
14911\,939.7289.5550007029.27
1507029.2752.7250002081.99
a

Calculate the monthly interest rate charged on this loan. Write your answer as a percentage to two decimal places.

b

Complete the next row of the table for month 151, rounding your answers to two decimal places.

c

How long, in years and months, did it take for them to pay off the loan?

d

Calculate the total repayments.

e

If they paid \$302\,097.60 in interest, how much did they initially borrow?

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