# Compound Interest Calculator

## How To Use Compound Interest Calculator

Lets first understand, what is compound interest and how we can calculate 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. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding.

The compounding frequency is the number of times per year, the accumulated interest is paid out

The compounding frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily.

Calculation of Compound Interest

1. Periodic compounding

$$Amount=P\biggl(1+\frac{r}{n}\biggr)^{nt}$$

where,

P is the original principal sum,

r is the annual interest rate,

n is the compounding frequency,

t is the overall time and

A is the amount.

$$Compound\hspace{0.1cm}Interest=Amount-Principal\hspace{0.1cm}Sum$$

Example 1: Calculate the compound interest for the sum $10000 with 5% annual rate of interest, compounded quarterly for 2 years. Solution:Here, P =$ 10000, r = 5%, t = 2 years and n = 4

$$Amount=10000\biggl(1+\frac{0.05}{4}\biggr)^{8}$$ $$Amount=10000*1.1045$$ $$Amount=\hspace{0.1cm}11042.60$$ $$Compound\hspace{0.1cm}Interest=\hspace{0.1cm}11042.60-\hspace{0.1cm}10000$$ $$Compound\hspace{0.1cm}Interest=\hspace{0.1cm}1042.60$$

Example 2: Calculate the compound interest for the sum $10000 with 5% annual rate of interest, compounded half yearly for 2 years. Solution:Here, P =$ 10000, r = 5%, t = 2 years and n = 2

$$Amount=10000\biggl(1+\frac{0.05}{2}\biggr)^{4}$$ $$Amount=\hspace{0.1cm}11038.13$$ $$Compound\hspace{0.1cm}Interest=\hspace{0.1cm}11038.13-\hspace{0.1cm}10000$$ $$Compound\hspace{0.1cm}Interest=\hspace{0.1cm}1038.13$$

2. Continuous compounding

As n, the number of compounding periods per year, increases without limit, the case is known as continuous compounding.

The amount after t periods of continuous compounding can be expressed in terms of the initial amount P0 as

$$P(t)=P_0e^{rt}$$

For calculating compound interest using above compound interest calculator, you have to just fill the given input boxes and press the calculate button, you will get compound interest and amount based on your entries.