Compound Interest Calculator

How to Calculate Compound Interest: Step-by-Step Example

Let's calculate the future value of an investment with the following parameters:

• Principal Value: \( P = \text{\$}1{,}000 \)
• Annual Interest Rate: \( r = 0.05 \) (5%)
• Investment Duration: \( t = 10 \) Years
• Annual Compounding Frequency: \( n = 12 \) (Monthly)
• Regular Contribution: \( c = \text{\$}100 \)
• Contribution Frequency: \( f = 12 \) (Monthly)

The future value (FV) is calculated using this formula:

$$ FV = P \cdot \left(1 + \frac{r}{n}\right)^{nt} + c \cdot \frac{\left(1 + \frac{r}{f}\right)^{ft} - 1}{\frac{r}{f}} $$ $$ = 1000 \cdot \left(1 + \frac{0.05}{12}\right)^{12 \cdot 10} + 100 \cdot \frac{\left(1 + \frac{0.05}{12}\right)^{12 \cdot 10} - 1}{\frac{0.05}{12}} $$ $$ = 1647.01 + 15528.23 = 17175.24 $$

Therefore, the future value of this investment is approximately $17,175.24.