Simple and compound interest

Simple interest#

Let principal be P, annual rate as a decimal be r, and time in years be t. Simple interest is P × r × t.

For 10,000 at 6% per year for 3 years, interest is 10,000 × 0.06 × 3 = 1,800. The final amount is 11,800.

Compound growth#

Compound interest calculates each period's growth on the amount already accumulated. With annual compounding, the amount after t years is P(1 + r)^t.

For 10,000 at 6% for two years:

• after year one: 10,600;
• after year two: 10,600 × 1.06 = 11,236.

The second year's interest includes growth on the first year's interest.

Match the periods#

If a rate is monthly, time must be counted in months. When compounding occurs several times per year, the rate per period and number of periods both change. Use only the convention stated in the question.

Common mistakes#

Do not confuse interest with final amount. Do not apply the full annual rate every month. And do not use the simple-interest formula when the balance compounds.

Compare methods#

For a positive rate and more than one period, compound interest normally exceeds simple interest because the base grows. For a single period at the same rate, the two give the same result.

Final check#

Estimate the scale of growth and verify that the amount remains above the principal for positive interest. State the assumed compounding period.