# 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.**
- Annual Compound Interest Formula:

Amount = P(1+R/100)^{n}
**Note- if interest is calculated annually, then compound interest is equal to simple interest**

- 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.**

- 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}

- 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)
- 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+R_{1}100)(1+R_{2}100)(1+R_{3}100)

- Present worth of Rs. x due n years hence will be:

Present Worth = x/(1+(R/100))^{n}