๐ Compound Interest Calculator
Enter the principal, annual interest rate, period, and compounding frequency to calculate compound interest and final amount.
How Compounding Works
Compound interest pays interest on interest. Each period the earned interest is added to the balance, so the next period is calculated on a larger base โ which is why a 5% annual return does not simply add 5% a year. The more often interest is compounded, the higher the effective rate for the same nominal rate: 5% compounded monthly yields about 5.12% a year, and daily compounding about 5.13%.
Compound Interest Formula
A = P ร (1 + r/n)nt
- P: Principal
- r: Annual interest rate
- n: Compounding frequency per year
- t: Investment period (years)
Compound interest adds earned interest back to the principal, so future interest is calculated on a larger base. You earn more than simple interest at the same rate.
A = P ร (1 + r รท n)^(n ร t), where P is the principal, r the nominal annual rate as a decimal, n the compounding periods per year and t the number of years. Total interest is A โ P. With continuous compounding the formula becomes A = P ร e^(r ร t).
Worked Examples
10,000 at 3.5% for 5 years, compounded annually โ 10,000 ร 1.035^5 = 11,876.86
The same investment compounded monthly โ 10,000 ร (1 + 0.035 รท 12)^60 = 11,909.37
What Compounding Ignores
The calculation assumes a constant rate and no withdrawals. In practice tax on interest, account fees and inflation all reduce real growth: at 3% inflation a 3.5% nominal return is only about 0.5% in purchasing power. Compounding also works against you on debt, where unpaid interest is added to the balance and starts earning interest itself.
Frequently Asked Questions
- What is the difference between the nominal and the effective rate?
- The nominal rate is the quoted annual rate; the effective rate is what you actually earn after compounding. At 5% nominal, monthly compounding gives 5.12% and daily compounding 5.13% effective.
- How long does it take to double my money?
- Use the rule of 72: divide 72 by the annual return. At 6% money doubles in about 12 years; at 9%, about 8 years. The rule is accurate to within a few percent for rates below about 10%.
- Does compounding frequency matter much?
- Less than people expect. At 5% over 10 years, annual and daily compounding differ by only about 0.3% of the final balance; the rate and the time matter far more.