Compound Interest Calculator
See how your savings grow when interest earns interest over time.
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Result
The formula
A = final amount, P = principal, r = annual rate, n = compounds per year, t = years.
Worked example
- P = $10,000, r = 5%, n = 12, t = 10
- A = 10000 × (1 + 0.05/12)^120
- A ≈ $16,470
Result: Final: $16,470
How compound interest is calculated
Compounding reinvests earned interest so later periods calculate interest on a larger base. The standard formula assumes a fixed rate and no extra deposits or withdrawals.
Variables
P is starting principal. r is the nominal annual rate as a decimal (5% → 0.05). n is compounds per year (12 = monthly, 365 ≈ daily). t is time in years. A is the ending amount.
Nominal rate vs. effective rate
The advertised rate is often nominal. The effective annual rate folds in compounding frequency: effective = (1 + r/n)^n − 1. Compare savings products on effective yield when frequencies differ — US disclosures often highlight APY for that reason.
Frequency matters, then plateaus
Moving from annual to monthly compounding can noticeably raise the final balance. Moving from daily to continuous compounding usually adds only a small extra amount at typical retail rates.
What this does not model
Fixed monthly contributions, account fees, taxes, and variable rates need a different approach (for example a savings-goal tool or a spreadsheet). Inflation reduces purchasing power even when the nominal balance rises.
Interesting facts
Einstein's quote?
Compound interest is often called the eighth wonder of the world — whether Einstein said it is debated, but the math is real.
APY vs. APR
In the US, savings ads often quote APY (includes compounding). Loan ads quote APR (includes certain fees). They answer different questions — do not mix them when comparing products.
Time beats rate hunting alone
Starting earlier usually outweighs waiting for a slightly higher rate. A decade of compounding often matters more than a half-point difference for a few years.
Fees silently reverse compounding
Account fees, expense ratios, and early-withdrawal penalties can erase years of interest growth. Always net the advertised rate against costs.
Frequently asked questions
Interest calculated on both the initial principal and interest already credited from earlier periods.
Yes, for the same nominal rate — more frequent compounding raises the effective yield. The jump from annual to monthly is larger than from daily to continuous at typical rates.
No. This calculator grows a single starting balance. For recurring contributions, use a savings-goal or contribution schedule tool.
Before tax and fees. Taxable interest, retirement-account rules, and inflation are outside the formula.
References
- Compound interest — definition Educational explanation of compounding frequency and growth.
- Time value of money basics Consumer-facing overview of interest, compounding, and long-term saving.