Section 9-7

Compound Interest

Imagine you put $100 in a savings account with a yearly interest rate of 6%.

After one year, you have 100 + 6 = $106. After two years, if the interest is simple, you will have 106 + 6 = $112 (adding 6% of the original principal amount each year.) But if it is compound interest, then in the second year you will earn 6% of the new amount:

1.06 × $106 = $112.36

YEARLY COMPOUND INTEREST FORMULA

If you put P dollars in a savings account with an annual interest rate r, and the interest is compounded yearly, then the amount A you have after t years is given by the formula:

A = P(1 + r)^t

Here, P = 4000, r = 0.07, and t = 5. Substituting the values in the formula, we get:

A = 4000(1 + 0.07)⁵

A 4000(1.40255)

A 5610.206

Rounding to the nearest cent, you have $5610.21.

GENERAL COMPOUND INTEREST FORMULA

If interest is compounded more frequently than once a year, you get an even better deal. In this case you have to divide the interest rate by the number of periods of compounding.

If you invest P dollars at an annual interest rate r, compounded n times a year, then the amount A you have after t years is given by the formula:

Here P = 1000, r = 0.09, n = 12, and t = 1.5 (since 18 months = one and a half years).

Substituting the values, we get:

A 1000(1.1439603)

A 1143.9603

Rounding to the nearest cent, you have $1143.96.