Compound Interest Calculator
See how savings or investments grow when interest earns interest. Add regular deposits to see the full picture.
Calculate
Future value
The formula
Future value compounds the starting balance, then adds the future value of regular deposits when you contribute each period.
Worked example
- P = $10,000, r = 5%, n = 12 (monthly), t = 10, no deposits
- A = 10000 × (1 + 0.05/12)^120 ≈ $16,470.09
- Interest ≈ $6,470.09; effective annual rate ≈ 5.12%
Result: Future value: $16,470.09
How compound interest is calculated
Compounding reinvests earned interest so later periods calculate interest on a larger base. Optional deposits use a standard future-value-of-annuity term at the same compounding frequency.
Core variables
P is the starting amount. r is the nominal annual rate as a decimal (5% → 0.05). n is compounds per year (12 = monthly). t is time in years. PMT is the deposit per compounding period (a monthly deposit is converted when n ≠ 12).
Beginning vs end of period
Deposits at the start of each period (annuity due) earn one extra period of interest versus deposits at the end (ordinary annuity). The calculator multiplies the annuity term by (1 + r/n) when that option is on.
Effective annual rate
Effective annual rate = (1 + r/n)^n − 1. Compare products on effective yield when compounding frequencies differ — US savings ads often highlight APY for that reason.
Inflation (optional)
When you enter an inflation rate, purchasing power is estimated as future value ÷ (1 + i)^t. That is a simple real-value sketch, not a full after-tax model.
What this does not model
Account fees, taxes, variable rates, and irregular deposits need a different approach. Rule-of-72 doubling time is a quick estimate (72 ÷ rate%), not a precise compound solve.
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.
Rule of 72
Divide 72 by the annual rate (%) for a rough doubling time — at 6%, about 12 years. It is a teaching shortcut, not a substitute for the exact formula.
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.
Yes. Enter an optional monthly deposit; it is converted to a per-period contribution matching your compounding frequency. Tick “deposit at the start” if contributions earn interest in the same period.
Before tax and fees. Taxable interest, retirement-account rules, and product costs are outside the formula. Inflation adjustment is optional purchasing-power only.
A common form is A = P(1 + r/n)^(nt). With regular deposits the future value adds an annuity term. This calculator shows both with a clear breakdown.
More frequent compounding helps, but the jump from annual to monthly is usually larger than from monthly to daily at the same nominal rate. Always compare APY (or effective annual rate) when offers use different schedules.
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.