Compound Interest Calculator

Simple interest pays you the same amount every year. Compounding pays you interest on your interest, so each period starts from a slightly larger balance than the last. That difference is small in year one and enormous by year thirty.

Notice that the first row is identical. Over a single period, compounding changes nothing - the advantage only exists because interest is being reinvested rather than paid out.

• P - principal. What you start with.
• r - annual rate as a decimal. 5% becomes 0.05. This is the nominal rate, the number advertised on the product.
• n - compounding frequency. How many times a year interest is calculated and added. Monthly is 12, daily is 365, quarterly is 4.
• t - time in years.
• A - the final amount, principal plus all interest earned.

The exponent nt is what does the work: it is the total number of times interest has been applied over the whole term. A longer term does not just add more periods, it raises the number of periods to a power.

Note. n matters far less than t. Switching from annual to daily compounding on 5% over ten years adds roughly 0.13 percentage points of yield. Extending the term from ten to twenty years nearly doubles the interest. Time is the dominant variable.

Both accounts pay 5% nominal interest. The only difference is how often interest is applied.

The spread between annual and daily compounding is $197.69 over a decade - noticeable, but nothing next to the $6,288.95 the money earned anyway. When you compare products, the headline rate and the term matter more than the compounding frequency, unless the rate is high or the term very long.

The result depends heavily on when you look. The same daily-compounded account shows $10,512.67 after one year, $11,051.66 after two, and $16,486.65 after ten. There is no single "return" - the return is a function of time.

1. Compounding an annual rate that is already an APY. If a bank quotes 5.12% APY, that figure already includes compounding. Applying the compounding formula to it again overstates your balance. APY is the yield you actually receive; nominal rate is the input to the formula.
2. Forgetting that the formula assumes no withdrawals. Every withdrawal removes money that would otherwise have compounded. On an investment this is silent and gradual; on a savings account it is immediate.
3. Assuming compounding works for you in debt. The same mathematics runs against you on credit cards and revolving balances. Compounding on a balance you are not paying down is what makes high-interest debt escalate so quickly.
4. Ignoring fees. A 0.5% annual management fee does not cost you 0.5% of your balance. It costs you 0.5% of your balance every year, permanently, and therefore compounds as a drag. Over thirty years at 7% growth, a 0.5% fee reduces the final balance by roughly 14%.
5. Using whole numbers for the rate. Entering 5 instead of 0.05 produces a figure one hundred times too large. If your answer looks implausible, check this first.

Three different numbers get called "the rate", and mixing them up is the most common cause of an incorrect result.

• Nominal rate is the stated annual rate before compounding. It is the correct input to the formula, because the formula applies the compounding itself.
• APY (annual percentage yield) is what you actually earn after compounding. It is always equal to or higher than the nominal rate. Use APY to compare savings products directly - it already accounts for frequency.
• APR is a borrowing figure that under US rules generally excludes compounding, though it may include fees. Use it to compare loans, not to project savings.

A practical shortcut: if you enter a nominal rate, use n as it is stated. If you are given an APY and want to project growth, you can treat it as an annual rate with n = 1, because the compounding is already baked in. Doing both - entering an APY and setting n to 12 - double-counts and inflates the projection.

This calculator produces a fixed-rate, fixed-term projection. Real products deviate in several predictable ways:

• Variable rates. Savings accounts, money market funds and many bonds reprice. The single rate here assumes it never changes for the whole term.
• Contributions and withdrawals. Adding money mid-term accelerates growth; withdrawing slows it. Neither is modelled in a lump-sum calculation.
• Tax. Interest is generally taxable in the year it is credited. A 5% return taxed at 25% nets 3.75%, and that reduction compounds too.
• Inflation. The figures are nominal - what you will see on a statement. What the money buys depends on inflation over the same period.
• Volatility. Any investment-based projection is an assumption, not a forecast. Bank deposits compound reliably; equities do not, and can finish well below the projected figure.

For savings you can control - regular deposits into an account - this model is close to correct. For investments, treat the output as a scenario rather than a prediction.