# What is compound interest?

**Compound interest**is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest

# How to calculate compound interest?

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

# What is formula of compound interest?

The mathematical formula for calculating compound interest **A = P(1 + r/n) ^{nt}**
In the formula:

**A**= Accrued amount (principal + interest)

**P**=Principal amount

**r**= Annual nominal interest rate as a decimal

**R**= Annual nominal interest rate as a percent

**r**= R/100

**n**= number of compounding periods per unit of time

**t**= time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years

## Compound interest formula to calculate accrued amount

**A = P(1 + r/n) ^{nt}**

## Compound interest formula to calculate principal amount

** P = A / (1 + r/n) ^{nt}**

## Compound interest formula to calculate rate of interest

** r = n((A/P) ^{1/nt} - 1)**

## Compound interest formula to calculate time

**t = (ln(A) - ln(P)) / n(ln(1 + r/n))**