Compound Interest Flashcards

All 7 cards in this deck

What is compound interest?

Interest worked out on the principal plus the interest already earned, so each year's interest is based on the new total.

What is the formula for the total amount in an account after compound interest?

e.g. £4500 for 2 years at 3.4% per year compound interest

$\text{Amount} = P \times \left(1 + \dfrac{r}{100}\right)^n$

$4500 \times 1.034^2 = £4811.20$

What are the steps to work out the amount of interest only for compound interest?

e.g. £4500 for 3 years at 1.8% per year compound interest

1. Write the multiplier: $1.018$
2. Find the total amount: $4500 \times 1.018^3 = £4747.40$
3. Subtract the principal: $4747.40 - 4500 = £247.40$

What are the steps to compare a simple interest account with a compound interest account?

e.g. £1000 for 3 years at 2% simple or 2% compound

1. Total for simple: $1000 + 3 \times 20 = £1060$
2. Total for compound: $1000 \times 1.02^3 = £1061.21$
3. Compare: compound is better, by £1.21

True or false? Investing at 5% compound interest for 2 years gives the same total as a single 10% increase.

False. The second year's interest is worked out on the larger amount, so compound interest gives more.

What are the steps to find the value of an investment when the rate of compound interest changes part-way through?

e.g. £7000 for 2 years: 3% in year 1, then 1.5% in year 2

1. Apply year 1's multiplier: $7000 \times 1.03 = 7210$
2. Apply year 2's multiplier to that answer: $7210 \times 1.015 = 7318.15$
3. Value at the end: £7318.15

True or false? If an account pays 3% in year 1 and 1.5% in year 2, you can add the rates and use a single multiplier of $1.045$.

False. You multiply the two multipliers: $1.03 \times 1.015 = 1.04545$.