# Compound Interest Formula and Facts

## What is 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.

Let Principal = P , Rate = R % per annum and Time = n years.
1. Annual Compound Interest Formula:
Amount = P(1+R/100)n

Note- if interest is calculated annually, then compound interest is equal to simple interest

2. Half Yearly Compound Interest Formula: When interest is compounded half yearly, then
Amount = P[1+(R/2)/100]2n

Note-When the interest is compounded (interest calculated and added to principal) half yearly, then the rate will be half and time will be twice.

3. Quarterly Compound Interest Formula:
When interest is compounded Quarterly, then
Amount = P[ 1+(R/4)/100]4n

Note-when the interest is compounded quarterly, then rate will be quarter and time will be 4 times.

Note-When the interest is compounded monthly,

then A=P{1+(r/1200)}12n

4. When interest is compounded Annually but time is in fraction, say 3(2/5)years.
then Amount will be,
Amount = P(1+R/100)3 x (1+(2R/5)/100)
5. When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively. Then Amount will be,
Amount=P(1+R1100)(1+R2100)(1+R3100)
6. Present worth of Rs. x due n years hence will be:
Present Worth = x/(1+(R/100))n