Interest earns its own interest

Mathematics · Ratio & Proportion · ages 15-16

Name ______________________ Date ____________

A machine is worth $12,000. It loses 10% of its value every year. Which expression correctly gives its value after n years?
- 12000 x (0.9)^n
- 12000 x (0.1)^n
- 12000 - 1200n
- 12000 x (1.1)^n
A town has 4,000 people. The population grows by 6% every year. Which expression gives the population after t years?
- 4000 x (1.06)^t
- 4000 x (0.06)^t
- 4000 + 1.06t
- 4000 x (1.6)^t
True or False: With simple interest, the amount of money added each year stays the same, but with compound interest, the amount added each year gets bigger over time.
Circle one: True False
With simple interest, the same amount of money is added every year.
Circle one: True False
Which grows savings faster over several years: simple or compound interest?
- Compound
- Simple
- Both grow equally
A city's population is 25,000 and grows by 2.5% each year. What will the population be after 5 years? Round to the nearest whole person.
Answer: ______________
A bank account earns simple interest of 4% per year on a $1000 deposit. How much interest is earned in year 3 alone?
Answer: ______________
A car is bought for $18,000. Every year it loses 15% of its current value. What is the car worth after 4 years? Round to the nearest dollar.
Answer: ______________
A chemical sample starts at 800 grams and loses 20% of its mass every hour. After how many whole hours will the sample first drop below 200 grams?
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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12000 x (0.9)^n · Losing 10% each year leaves 90% of the value, so the multiplier is 0.9, and it gets raised to the power n for n years.
4000 x (1.06)^t · Growing by 6% each year means multiplying by 1.06 every year, so the multiplier gets raised to the power t.
True · Simple interest is based only on the starting amount, so it adds a fixed amount every year. Compound interest is based on the current balance, so the yearly amount added keeps growing.
True · Simple interest pays only on the original amount, so the addition never grows.
Compound · Compound pays on the growing balance, so its yearly additions keep growing.
28285 · Growing by 2.5% each year means multiplying by 1.025 every year, so after 5 years you multiply by 1.025 five times.
40 · Simple interest always uses the original deposit, so the same amount of interest is earned every single year, including year 3.
9396 · Losing 15% each year means multiplying by 0.85 every year, so after 4 years you multiply by 0.85 four times.
7 · Losing 20% each hour means multiplying by 0.8 every hour. Trying whole numbers of hours shows the sample first dips below 200 grams at hour 7.
6 · Trial powers of 0.88: 500 times 0.88^6 first lands below 250.