Compound Interest Calculator: How Savings Grow Over Time

Compound interest means earning interest on an initial balance and, over time, on previously earned interest. It can affect savings, investments and debt. The actual result depends on the rate, compounding schedule, fees, taxes and whether contributions or withdrawals occur.

Compound interest formula

For a fixed nominal annual interest rate and no additional contributions, the standard formula is:

A = P × (1 + r/n)^nt

Where A is the future balance, P the initial principal, r the nominal annual rate as a decimal, n the number of compounding periods per year, and t the number of years.

Worked example

Imagine depositing $1,000 at a nominal annual interest rate of 5%, compounded annually for three years, with no fees, taxes or extra deposits.

A = 1,000 × (1.05)³ = $1,157.63 (rounded). Interest earned is approximately $157.63.

Does compounding frequency matter?

At the same nominal annual rate, more frequent compounding generally produces a slightly higher balance. Annual, monthly and daily compounding therefore do not necessarily give identical outcomes. When comparing accounts, check the annual percentage yield (APY) or equivalent effective annual rate rather than comparing nominal rates alone.

What about monthly contributions?

Regular deposits require an additional contribution calculation. Results differ depending on whether deposits occur at the beginning or end of each period. A calculator should state its assumption clearly.

Inflation, taxes and fees

A future account balance is a nominal amount. Inflation can reduce its purchasing power, while taxes and account fees may reduce the amount retained. Investment returns are not guaranteed and may fluctuate; the fixed-rate formula is an illustration rather than a forecast.

Common calculation mistakes

• Entering 5 instead of 0.05 for a 5% rate in a manual formula.
• Confusing nominal annual interest with APY.
• Assuming contributions occur at the start rather than the end of each period.
• Ignoring fees, inflation or variable interest rates.
• Using a savings formula to predict uncertain investment returns.

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FAQ

Is compound interest the same as simple interest?

No. Simple interest is calculated only on the original principal, while compound interest can also accrue on prior interest.

Does this formula work for every investment?

No. It models a constant rate and specified compounding schedule. Real-world investment returns can vary and may include losses.