Compound Interest
Compound Interest refers to the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. This means that interest is earned on both the original amount and the interest that has been added to it, leading to Exponential Growth over time.
The formula for calculating compound interest is:
A = P (1 + r/n)^(nt)
- A = the Future Value of the investment/loan, including interest
- P = the principal investment amount (initial deposit or loan amount)
- r = the annual Interest Rate (decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the Money is invested or borrowed for
Example 1: If you invest $1,000 at an annual Interest Rate of 5% compounded annually for 3 years:
A = 1000 (1 + 0.05/1)^(1*3) = 1000 (1.05)^3 ≈ $1,157.63
Example 2: If you invest $1,000 at an annual Interest Rate of 5% compounded monthly for 3 years:
A = 1000 (1 + 0.05/12)^(12*3) = 1000 (1 + 0.0041667)^(36) ≈ $1,161.62
Case: If two people invest $5,000 at the same annual Interest Rate of 6%, but one compounds annually while the other compounds quarterly for 10 years:
- Annually: A = 5000 (1 + 0.06/1)^(1*10) ≈ $8,144.97
- Quarterly: A = 5000 (1 + 0.06/4)^(4*10) ≈ $8,287.23
This shows that more frequent compounding leads to a higher amount of accumulated interest.