Simple interest

Money has a price for being borrowed or lent, and that price is interest. The simplest way to charge it is simple interest, where interest is calculated only on the original amount — the principal — and never on interest already earned.

The formula

Let PV be the present amount (principal), i the interest rate per period, and n the number of periods. The interest earned and the final amount are:

Interest = PV * i * n
FV = PV * (1 + i * n)

The rate i must match the period of n. A rate of 2% per month with n in months, or 12% per year with n in years.

Worked example

You deposit R$ 1,000 at 1% simple interest per month for 6 months:

Interest = 1000 * 0.01 * 6 = 60
FV = 1000 * (1 + 0.01 * 6) = 1000 * 1.06 = 1,060

After 6 months you have R$ 1,060 — exactly R$ 10 of interest each month, because simple interest never compounds.

Where it shows up

Simple interest appears in short-term arrangements: some commercial discounts, certain late-payment fees, and quick back-of-the-envelope estimates. For anything spanning many periods, the next lesson — compound interest — is what the real world uses, and the difference grows large with time.