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5.07 Modelling with compound interest

Worksheet
Compound interest models
1

How much will it cost to buy a computer in 7 years if the annual inflation rate is 8\% and it currently sells for \$640?

2

The most recent valuation of a famous painting was 16 years ago, when it sold for \$670\,000 at auction. If the value of the painting has appreciated at 4.5\% p.a., how much is the painting worth today? Round your answer to the nearest dollar.

3

A house was valued 8 years ago to be worth \$498\,000. Its value appreciated at 4.4\% p.a. What is its value today? Round your answer to the nearest dollar.

4

In 1996, a jar of Nutella costs \$4. The value inflated at an average rate of 2.3\% p.a. What would the cost have been in 2005?

5

The value of land is expected to grow by 5.1\% each year for the next 5 years. If it currently costs \$550 per square metre, how much will it cost at the end of 5 years?

6

If an estate appreciates at an average rate of 4.6\% p.a. and its current value is \$500\,000, calculate its value in 8 years. Round your answer to the nearest dollar.

7

Omah deposits \$4000 into a new savings account which increases by 7.1\% each year. Find the value of the deposit after 4 years, giving your answer correct to the nearest dollar.

8

The federal government wants to increase funding to a certain program over 4 years at a constant rate of 3.75\% p.a. over that time period. If the initial funding was \$14\,000\,000, find the value of the funding (to the nearest dollar) after:

a

The first year.

b

2 years.

c

4 years.

9

In terms of today’s dollar, find the value of \$14 in 13 years time if the inflation rate is:

a

5.2\%

b

7.2\%

10

A jacket today costs \$43.50. Calculate its price 3 years ago if the average inflation rate since then has been 5.1\% p.a.

11

An item costs \$10\,000 today. Calculate its price 7 years ago if the inflation rate has averaged 3.5\% p.a. since then. Round your answer to the nearest dollar.

12

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

13

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 initially?

14

Tina currently has 174 followers on her online business page. If the number of people following her is growing at a rate of 5\% per month, how many people will be following her business page in 6 months?

15

The population of a culture of bacteria is observed to grow each day by 0.55\% of the previous day’s population. The culture currently has a population of 800 units.

a

If the growth continues at this rate, what will be the population of the bacteria culture in 35 days? Round your answer to the nearest whole number.

b

Assuming the bacteria have been growing like this consistently, what was the population 11 days ago? Round your answer to the nearest whole number.

16

The area covered by an ice shelf is measured to be 1437\text{ km}^2, but records show that it has been decreasing by 2\% each year over the past decade.

a

What area was covered by the ice shelf 10 years ago, to the nearest square kilometre?

b

What has been the loss in the ice shelf’s area over the past decade?

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MS2-12-5

makes informed decisions about financial situations, including annuities and loan repayments

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