Investment

What is compound interest?

Compounding reinvests prior interest or returns so future returns can earn returns of their own.

Definition

Compounding reinvests prior interest or returns so future returns can earn returns of their own.

Intuition

The longer the period, the more periods earlier gains have to grow.

Formula

FV = PV {(1 + \frac{r}{m})}^{m t} + \sum_{j = 1}^{12 t} PMT {(1 + \frac{r}{m})}^{\frac{(12 t - j) m}{12}}

Final value equals the compounded initial principal plus the accumulated value of each monthly contribution.

Example

Enter an initial investment of 100,000 and a monthly contribution of 5,000.
Set a 7% annual return, 10 years, and monthly compounding.
The result separates 700,000 of contributions from the modeled investment gain and final value.

Common mistakes

Do not treat a fixed return as guaranteed or confuse nominal and effective annual rates.