Compound Interest Calculator
See how your money grows over time with compound interest. Enter an initial amount, interest rate, time period, and optional recurring contributions.
| Year | Total Contributed | Interest Earned | Balance |
|---|
What is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only earns on the principal), compound interest causes balances to grow exponentially — the longer the time horizon, the more dramatic the effect.
Einstein is often (likely apocryphally) credited with calling compound interest "the eighth wonder of the world." Whether he said it or not, the math is remarkable. $10,000 invested at 7% for 30 years grows to roughly $76,000 with no contributions — at 40 years it becomes $150,000.
The Compound Interest Formula
For a lump-sum investment with no contributions:
A = P × (1 + r/n)^(n×t)
Where:
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (as a decimal)
- n = number of times interest compounds per year
- t = number of years
When you add regular contributions, each contribution earns compound interest from the time it is made. The calculator above handles this using a period-by-period loop for accuracy.
Compounding Frequency Matters
The more frequently interest compounds, the more you earn — though the difference narrows at higher frequencies:
| Frequency | $10,000 at 7% for 10 years |
|---|---|
| Annually | $19,671.51 |
| Quarterly | $19,889.24 |
| Monthly | $20,096.61 |
| Daily | $20,137.48 |
Monthly compounding is the most common in savings accounts and investment accounts. Daily compounding is common with high-yield savings accounts.
The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
At 6% interest: 72 ÷ 6 = 12 years to double.
At 9% interest: 72 ÷ 9 = 8 years to double.
The Rule of 72 works well for rates between 4% and 20%.
Compound Interest vs. Simple Interest
| Simple Interest | Compound Interest | |
|---|---|---|
| Interest earned on | Principal only | Principal + accumulated interest |
| Growth shape | Linear | Exponential |
| Common use | Short-term loans, bonds | Savings, investments, mortgages |
| $10k at 7% for 20 years | $24,000 | $38,697 |
Frequently Asked Questions
What interest rate should I use?
For long-term stock market projections, 7% is a commonly cited historical average real return (inflation-adjusted) for a diversified US stock index. Nominal returns have averaged around 10%. For savings accounts or CDs, use the actual APY quoted by your bank.
Does this calculator account for taxes?
No. In taxable accounts, investment gains are subject to capital gains tax each year (or when sold), which reduces your effective return. In tax-advantaged accounts like a 401(k) or IRA, taxes are deferred or eliminated. For long-term projections, consider reducing the rate by your estimated tax drag.
What is APY vs. APR?
APR (Annual Percentage Rate) is the stated rate before compounding. APY (Annual Percentage Yield) reflects the actual return after compounding is applied. A 7% APR compounded monthly equals a 7.229% APY. Banks are required to disclose APY on deposit accounts in the US.
How does this relate to a mortgage?
Mortgages use compound interest in reverse — your balance decreases over time as you make payments. Each payment covers accrued interest first, with the remainder reducing principal. The Mortgage Payment Calculator shows the full amortization breakdown for a home loan.
