Compound Interest Calculator

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Results

  • Total Principal:
  • Interest Amount:
  • Balance:
  • APY:

Compound Interest Concept


Compounding

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


Compound Interest

Compound interest is interest on interest. Compound interest is not the result 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:

\[ I = 12 \times \left(1 + \frac{R}{N}\right)^{\frac{N}{12}} \]

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

\[ B_0 = P, \quad B_n = B_{n-1} + \bigl(B_{n-1} + PMT\bigr) \times \frac{I}{12}. \]

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

\[ B_0 = P, \quad B_n = B_{n-1} + \bigl(B_{n-1} \times \frac{I}{12}\bigr) + PMT. \]

Finally,

\[ B = \sum_{i=1}^{T \times 12} B_i \]
\[ P_f = P + T \times (PMT \times 12) \]
\[ APY = \left(\left(1 + \frac{R}{N}\right)^N - 1\right) \]

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