Compound Interest Calculator

Compound Interest Concept

Definitions - Compound Interest

Compounding

If accumulated intereset is added back to the principal, it is called compounding [1].

Compound Interest

Compound interest is related with the word "compound". So we can define compound interest as interest on interest. Compound interest is not resut of paying it out, in contrast, it is the result of investing interest again(reinvesting) [2]. Compound interest is an important topic in finance and economics.

Compound Interest Formula - How to Calculate Compound Interest

Let

$P$ = Principal Amount
$PMT$ = Monthly Payment
$R$ = Annual Rate
$T$ = Number of Years
$N$ = Compounding

$I$ = Rate compounded monthly
$B_i$ = Balance at the month i
$B$ = Final Balance
$P_f$ = Total Principal
$C$ = Interest Amount
$APY$ = Annual Percentage yield.

First, calculate the rate compounded monthly:

If payments are made at the begining of the period, then

If payments are made at the end of the period, then

Finally,

Examples

Example 1

Input

Principal Amount = 5000
Monthly Payment = 100
Annual Rate = 5%
Number of Years = 10
Compounding = 4 (Quarterly)
Mode = BEG

Output

Total Principal = 17000
Interest Amount = 6793.511
Balance = 23793.511
Apy = 5.095%

Example 2

Input

Principal Amount = 1000
Monthly Payment = 200
Annual Rate = 3%
Number of Years = 6
Compounding = 12 (Monthly)
Mode = END

Output

Total Principal = 15400
Interest Amount = 1552.826
Balance = 16952.826
Apy = 3.042%

References

1. A Basic Course in the Theory of Interest and Derivatives Markets (n.d). http://faculty.atu.edu/ mfinan/actuarieshall/mainf.pdf

2. Compound Interest (n.d.). Retrieved August 18, 2016, from https://en.wikipedia.org/wiki /Compound_interest