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7.03 Applications of compound interest

Worksheet
Appreciation
1

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

2

The value of a piece of land is expected to grow by 6.8\% each year for the next 5 years. If it currently costs \$460 per square metre, calculate its value at the end of 5 years.

3

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?

4

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.

5

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.

6

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.

7

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

8

A car enthusiast purchases a vintage car for \$220\,000. Each year, its value increases by 12 percent of its value at the beginning of the year. Find the value of the car after 7 years.

Inflation
9

Calculate the value of a \$1330 brand new desk after 7 years if the annual inflation rate is 11\%.

10

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.?

11

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

12

The price of a movie ticket 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?

13

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.

14

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\% p.a.

b

4.1\% p.a.

Exponential growth
15

A country's population of 18 million people is expected to increase by 2.1\% p.a. over the next 38 years. Calculate the expected population in 38 years time.

16

A scientist observed that a certain species of bacteria grew by 13\% each hour. How many bacteria will be present after 17 hours if there were 79 bacteria initially?

17

The population of Joanne's home town is 27\,400 and has a growth rate of 6\% each year.

a

Find the size of the population after 7 years.

b

How many more people will be in the town after 10 years?

18

The population of cows at a free range farm has a growth rate of 17\% p.a. If the farm originally has 140 cows, how many will there be after 4 years?

19

Tina currently follows 174 people on Twitter. The number of people she follows is growing at a rate of 5\% per month. How many people will she be following in 6 months?

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Outcomes

4.3.1.3

consider similar problems involving compounding [complex]

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