Compound Interest

Compound Interest

Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound interest can be thought of as “interest on interest,” and will make a deposit or loan grow at a faster rate than simple interest, which is interest calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period. Compound interest is also known as compounding.

The formula for calculating compound interest is:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

= [P (1 + i)ⁿ] – P

= P [(1 + i)ⁿ – 1]

(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)

If the number of compounding periods is more than once a year, "i" and "n" must be adjusted accordingly. The "i" must be divided by the number of compounding periods per year, and "n" is the number of compounding periods per year times the loan or deposit’s maturity period in years.

For example:

• The compound interest on $10,000 compounded annually at 10% (i = 10%) for 10 years (n = 10) would be = $25,937.42 - $10,000 = $15,937.42
• The amount of compound interest on $10,000 compounded semi-annually at 5% (i = 5%) for 10 years (n = 20) would be = $26,532.98 - $10,000 = $16,532.98
• The amount of compound interest on $10,000 compounded monthly at 10% (i = 0.833%) for 10 years (n = 120) would be = $27,070.41 - $10,000 = $17,070.41