# Compound interest

Compound interest is calculated as ‘interest on interest’ as well as interest on the original principal amount.

Compound interest per year is the usual quotation basis for periods of more than a year.

To calculate compound interest for different periods we compound up or de-compound the interest depending on the relative lengths of the periods being considered.

**Example 1**

Interest quoted at 6% per annum,

compounded annually,

for two years maturity,

with all of the interest paid at the final maturity,

means that the interest paid after two years will be (compounding up for two periods):

= (1.06 x 1.06) - 1

= 12.36% periodic interest for the two year period.

Decompounding is used to calculate periodic interest for a shorter period.

**Example 2**

If periodic interest is 12.36% for a two-year period, this means the total accumulated interest payable/receivable at the end of the two years is 12.36%.

Decompounding the 12.36% (per two years) to calculate the interest for just one year. One year's interest:

= (1 + 0.1236)^{(1/2)} - 1

= 6.00% per one-year period.