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VCE 11 General 2023

4.08 Interest applications

Worksheet
Investments
1

Dave's investment of \$6000 earns interest at 2\% p.a, compounded annually over 3 years.

Using repeated multiplication, find:

a

The value of the investment after 3 years.

b

The amount of interest earned.

2

A \$2090 investment earns interest at 4.2\% p.a. compounded annually over 17 years. Use the compound interest formula to calculate the value of this investment.

3

Sally's investment of \$8950 earns interest at 4\% p.a. compounded annually over 4 years. Find the amount of interest earned.

4

\$3900 is invested for three years at a rate of 10\% p.a., compounding annually.

a

Complete the table below to determine the final value of the investment:

Balance + interest Total balance Interest earned
First year-\$3900\$390
Second year\$3900 + \$390\$4290\$429
Third year
Fourth year -
b

Calculate the total interest earned over the three years.

5

State whether the following is true about compound interest:

a

Interest is earned on the principal.

b

The interest in any time period is calculated using only the original principal.

c

Interest is earned on any accumulated interest.

d

The amount of interest earned in any time period changes from one period to the next.

Inflation
6

What is the value of a \$1330 brand new desk after 7 years when the annual inflation rate is 11\%?

7

In 2001, the price of a bottle of orange juice was \$3.20. What was the price of a bottle of orange juice in 2006 if the inflation rate was 8\% p.a.?

8

For an inflation rate of 7.4\% per year, what is the expected value of a \$210 basket of groceries 7 years from now?

9

A one year sports club membership currently costs \$332. Calculate the cost in 6 years time if the inflation rate is 2.6\% per annum. Round your answer to the nearest dollar.

10

In terms of today's dollar, what will be the value of \$5 in 15 years time if the inflation rate is:

a

2.1\%

b

4.1\%

11

Find the original price of the following items:

a

A hat today costs \$35.50. Find the price of the hat 9 years ago at an inflation rate of 3.7\% per annum.

b

An item costs \$15\,000 today. Find the price of the item 4 years ago at an inflation rate of 3.5\% per annum.

12

The price of pens and pencils in 1996 was \$5. If the value inflated at an average rate of 3.2\% per annum, what would the price have been in 2005?

Appreciation
13

What is the value of a wine collection, currently valued at \$4790, after 10 years if its rate of appreciation is 9\% p.a.?

14

The value of land is expected to grow by 6.8\% each year for the next 5 years. If it currently costs \$460 per square metre, how much will it cost at the end of 5 years?

15

Due to dwindling supplies of oil, oil prices are expected to appreciate by 7.2\% p.a. If the current price of oil is \$79 a barrel, what is the expected price of a barrel in 23 years time?

16

A house was valued 6 years ago to be worth \$548\,000. Its value appreciated at 5.2\% p.a. What is its appreciated value? Give your answer to the nearest dollar.

17

If a piece of land appreciates at an average rate of 3.7\% per annum and its current value is \$430\,000, calculate its value in 3 years. Give your answer to the nearest dollar.

18

A high interest bank account deposit appreciates at 6.6\% per annum and is currently valued at \$46\,000. What will its value be in 8 years? Give your answer to the nearest dollar.

19

Sean deposits \$4000 into a new savings account. The amount increased by 3.3\% each year for 4 years. Find the new value of the deposit after appreciation, giving your answer to the nearest dollar.

20

The federal government wants to increase funding to a certain program over 8 years at a constant rate of 4.75\% per annum over that time period. If the initial funding was \$14\,000\,000, find the value of the funding (to the nearest dollar) after:

a

1 year

b

4 years

c

8 years

21

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

Depreciation
22

There were 10\,100 digital sales of a particular song in its first month of release. The number of monthly digital sales decreased by 360 each month after.

a

The song registered 7580 digital sales in a particular month. What was the decrease in the monthly sales from the first month?

b

In how many months after the initial month of release did the song register 7580 in monthly digital sales?

23

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

What was the annual depreciation using the straight-line method?

b

After 7 years, the robots are sold off. If they continue to depreciate at an annual rate of \$14\,000, how much can they be sold for?

24

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?

1
2
3
4
\text{Years}
9000
18000
27000
36000
\text{Value }(\$)
25

Marge purchased shares at a total value of \$99\,800. After 6 months, the shares had dropped in value to \$99\,200.

a

What is the monthly depreciation using the straight-line method?

b

Sketch the graph showing the depreciation of the value of the shares over 6 years.

c

What is the gradient of the line?

d

What does the gradient represent in context?

e

What is the value of the y-intercept of the line?

f

What does the y-intercept represent in context?

g

Let V represent the value of the shares after n months. Write the equation of the line.

h

Find the value of the shares after 5\dfrac{1}{2} years.

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Outcomes

U2.AoS4.8

scientific notation, exact and approximate answers, significant figures and rounding

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