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Compound Interest Made Simple

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Compound Interest Made Simple

Explore how savings can grow when interest is added to the balance. Show your calculations and round money to the nearest cent unless a question says otherwise.

The compound interest idea

Compound interest means interest is added to savings, and later interest is calculated on the new, larger balance. The formula is A = P(1 + r/n)^(nt). Here, P is the starting balance, r is the annual interest rate written as a decimal, n is the number of times interest is added each year, t is the number of years, and A is the final balance.

1.Match each symbol in the compound interest formula to its meaning.

Annual interest rate as a decimal
Final balance
Number of years
Starting balance
Number of times interest is added each year

2.A savings account pays 4% annual interest, added monthly. What values should be used for r and n in the formula?

r = 4 and n = 12
r = 0.04 and n = 12
r = 0.04 and n = 4
r = 12 and n = 0.04

End of year

Balance

$1,000.00

$1,050.00

$1,102.50

$1,157.63

3.Use the balance table above. How much interest was added during year 2?

4.Nathan puts $2,000 into an account paying 4% interest per year, compounded annually, for 5 years. Use A = P(1 + r/n)^(nt) to calculate the final balance. Round to the nearest cent.

5.Using the result from Question 4, how much interest did Nathan earn altogether? Subtract her starting deposit from the final balance.

6.With compound interest, the interest earned in one period can itself earn interest in later periods.

TrueFalse

7.Both options start with $1,000 for one year. Option A pays 7% interest compounded annually. Option B pays 6.5% interest compounded monthly. Calculate each final balance and decide which option gives more after one year. Round to the nearest cent.

8.Mele saves $500 at an annual interest rate of 6%, compounded monthly, for 2 years. Write down P, r, n and t, then calculate the final balance to the nearest cent.

9.In your own words, explain why compound interest can make a savings balance grow faster over time than earning interest only on the original deposit.