Compound interest is the interest on a loan or investment that is calculated based on both the initial principal and the accumulated interest from previous periods. This results in exponential growth over time.
1. Compound Interest Formula
The standard formula for compound interest is:
A = P (1 + r/n)^(nt)Where:
- A = Final Amount
- P = Principal (initial amount)
- r = Annual interest rate (decimal)
- n = Number of times interest compounds per year
- t = Number of years
2. Example of Annual Compounding
Scenario: You invest $5,000 at an annual interest rate of 6%, compounded once per year, for 5 years.
A = 5000 × (1 + 0.06/1)^(1×5)A = 5000 × (1.06)^5A = $6,691.133. Example of Monthly Compounding
Scenario: You invest $5,000 at a 6% annual interest rate, compounded monthly for 5 years.
A = 5000 × (1 + 0.06/12)^(12×5)A = 5000 × (1.005)^60A = $6,744.254. Daily Compounding Example
Scenario: You invest $5,000 at a 6% annual interest rate, compounded daily (365 times a year) for 5 years.
A = 5000 × (1 + 0.06/365)^(365×5)A = 5000 × (1.000164)^1825A = $6,747.135. The Power of Compound Interest
The more frequently interest compounds, the higher the final amount. Here’s a quick comparison of the same investment ($5,000 at 6% for 5 years):
- Annual Compounding: $6,691.13
- Monthly Compounding: $6,744.25
- Daily Compounding: $6,747.13