Compound interest formula

A simpler version of the compound interest formula is B  = P( 1 + r)ⁿ  where B is the final balance, P is the principal, r is the interest rate for 1 or each interest period, and n is the number of payment periods.

The principal is the amount of money you deposit that you expect will grow over time.

What do we mean by number of interest periods ?

The number of interest periods is the number of times the interest is computed per year.

If the interest is computed and added to the principal twice a year, this means that the number of interest periods is 2.

If the interest is computed and added to the principal four times a year, this means that the number of interest periods is 4.

What do we mean by number of payment periods ?

The number of payment periods is the total number of times interest is added to the principal. This is n is the formula.

If the number of interest periods is 2 and we do this for 3 years, then the number of payment periods is 2 times 3 or n =  6.

Suppose you invest $2000 that earns 8% annually compounded quarterly for 5 years. Find r and n.

Here is how to find r.

8% annual interest rate / 4 interest periods = 2% semiannual interest rate.

Here is the explanation.

The interest rate is computed quarterly or four times a year. 8% is the interest rate for the whole year or for 4 interest periods. Since r is the interest rate for 1 interest period, r = 8% / 4 = 0.08 / 4 = 0.02.

Here is how to find n.

n is the number of payment periods or total number of times interest is added to the principal.

Since there are 4 interest periods in a year and we do this for 5 years, then there are 4 times 5 or 20 payment periods.

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