Interest earns its own interest

Mathematics · Ratio & Proportion · ages 15-16

Name ______________________ Date ____________

A phone worth $800 loses 15% of its value each year. Which expression gives its value after n years?
- 800 x (0.85)^n
- 800 x (0.15)^n
- 800 - 120n
- 800 x (1.15)^n
A colony of 300 bacteria triples every hour. Which expression gives the number after h hours?
- 300 + 3h
- 300 x 0.3^h
- 300 x 3^h
- 3 x 300^h
Jo puts $200 in an account paying 5% simple interest, so she earns $10 every year. Ali puts $200 in an account paying 5% compound interest. True or false: in year 2, Ali earns more interest than Jo.
Circle one: True False
With simple interest, the same amount of money is added every year.
Circle one: True False
Two accounts start with the same positive savings and earn the same fixed positive yearly rate. One pays simple interest, the other compounds once a year. No money is added or withdrawn and there are no fees. Which has the larger balance after 2 years?
- Compound
- Simple
- Both grow equally
A town of 15000 people grows by 2% each year. What is its population after 3 years, to the nearest whole person?
Answer: ______________
Kofi deposits $2500 in an account paying 3% simple interest a year. How much interest does it earn in total over 4 years, in dollars?
Answer: ______________
A laptop bought for $1200 loses 25% of its value each year. What is it worth after 3 years, in dollars?
Answer: ______________
A 1000 litre tank loses 30% of its water each day. After how many whole days does it first hold less than 200 litres?
Answer: ______________
A pond has 500 fish. Fishing cuts the population 12% each year. After how many whole years does it first drop below 250?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

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800 x (0.85)^n · Losing 15% keeps 85%, so the multiplier 0.85 is raised to the power n.
300 x 3^h · Tripling means times 3 each hour, so the power of 3 counts the hours: 300 x 3^h.
True · Ali earns $10 in year 1, so his balance is $210. In year 2 he earns 5% of $210, which is $10.50, more than Jo's $10.
True · Simple interest pays only on the original amount, so the addition never grows.
Compound · Both earn the same interest in year 1. In year 2, compound interest also earns interest on year 1's interest, so its balance is larger.
15918 · Growing 2% a year means times 1.02 each year, so the population is 15000 x 1.02^3, about 15918.
300 · Simple interest pays 3% of the original $2500 every year, which is $75, so 4 years earn 4 x 75 = $300.
506.25 · Losing 25% keeps 75%, so multiply by 0.75 three times: 1200 x 0.75^3 = 506.25.
5 · Times 0.7 each day: day 4 leaves 240.1 litres and day 5 leaves about 168.1 litres, so day 5 is the first below 200.
6 · Trial powers of 0.88: year 5 gives about 263.9 and year 6 gives about 232.2, so year 6 is the first below 250.