Compound Interest Calculation
What is Compound Interest?
Compound interest refers to the interest that accumulates on both the initial principal and the interest already added to the principal. This type of interest leads to exponential growth of the investment as opposed to simple interest, which only grows linearly.
Formula for Compound Interest:
A = P × (1 + r/n)nt
Where:
- A = The final amount (principal + interest)
- P = The principal amount
- r = The annual interest rate (in decimal form)
- n = The number of times interest is compounded per year
- t = The time period in years
Step-by-Step Example
Investment Example:
Let’s say you invest $1,000 at an annual interest rate of 5%, compounded quarterly, for 3 years.
Given:
- P = 1000
- r = 0.05
- n = 4 (quarterly compounding)
- t = 3 years
Using the formula:
A = 1000 × (1 + 0.05 / 4)4 × 3
A = 1000 × (1.0125)12
A ≈ 1000 × 1.1616 = 1161.60
The compound interest earned is $161.60.
Why Compound Interest is Important
Understanding compound interest is essential for anyone looking to make their savings or investments work harder over time. The earlier you start investing, the more you can benefit from compound interest, which works in your favor the longer you leave your money invested.