How to Calculate Compound Interest
Hesaplayıcı2 min read
Short answer
Compound interest is interest that grows the principal at the end of every period, so the interest already added earns interest too. The formula is A = P × (1 + r/n)^(n × t). For example, 10,000 at 12% a year compounded monthly grows to about 11,268 after one year; simple interest at the same rate gives 11,200.
Formula
A = P × (1 + r/n)^(n × t)
- A: the final amount
- P: the principal
- r: the nominal annual rate as a decimal (0.12 for 12%)
- n: the number of compounding periods per year (1 yearly, 12 monthly, 365 daily)
- t: the term in years
Step-by-step example
A principal of 10,000, a nominal 12% a year, compounded monthly, for 1 year:
- Find the rate per period: 0.12 ÷ 12 = 0.01, that is 1% a month.
- Find the number of periods: 12 × 1 = 12.
- Find the growth factor: (1 + 0.01)^12 ≈ 1.126825.
- Multiply by the principal: 10,000 × 1.126825 ≈ 11,268.25.
The total interest is about 1,268.25.
The effect of compounding frequency
At the same nominal rate, the more often interest is added within a year, the higher the result. A principal of 10,000 at 12% a year for 1 year:
| Compounding | Final amount | Effective annual rate |
|---|---|---|
| Yearly | 11,200.00 | 12.00% |
| Monthly | 11,268.25 | 12.68% |
| Daily | 11,274.75 | 12.75% |
When you compare offers, compare the effective annual rate, not the nominal rate.
How it differs from simple interest
Simple interest applies to the principal only: A = P × (1 + r × t). When the term is longer than one compounding period, compound interest gives a higher amount, and the gap grows with the term. Over 10 years, simple interest gives 22,000 and monthly compounding about 33,004.
Worked example: 10,000 at 10% a year, compounded monthly, for 5 years
Final amount
16,453.09
- Total interest
- 6,453.09
- Nominal annual rate
- 10.00%
- Effective annual rate
- 10.47%
- Term
- 5 years
Step by step
Nominal annual rate
r = rate × periods per year
r = 10% × 1 = 10.00%
Term
t = years + months/12 + weeks/52 + days/365
t = 5 + 0/12 + 0/52 + 0/365 = 5 years
Final amount
A = P × (1 + r/n)^(n × t)
A = 10,000 × (1 + 10%/12)^(12 × 5) = 16,453.09
Effective annual rate
e = (1 + r/n)^n − 1
e = (1 + 10%/12)^12 − 1 = 10.47%