Interest Calculator

Interest is what a borrower pays a lender for the use of money, quoted as a rate or a flat amount. It runs underneath almost every loan, savings account, and bond. This calculator shows how a starting amount grows once interest is added on top, with room for regular deposits, a tax rate on the earnings, and inflation. Money grows two different ways, by simple interest or by compound interest, and the gap between them is the whole story.

Simple interest

Start with the plainest case. Derek borrows $100, the principal, from a bank for one year at 10%. The interest is $100 × 10% = $10, so a year later he repays $110, the $100 principal plus $10 interest. Stretch the loan to two years and the bank charges the same 10% each year: $100 + $10 (year 1) + $10 (year 2) = $120, or $100 principal and $20 interest.

The formula behind it is short:

interest = principal × rate × term

Simple interest almost never shows up in real accounts, though. When people say "interest" in daily life, they usually mean interest that compounds. Our Simple Interest Calculator covers the flat version on its own.

Compound interest

Compounding needs more than one period, so go back to Derek's two-year loan at 10%. Year one works as before: $100 × 10% = $10, and the balance becomes $110. Year two is where it changes. Instead of charging 10% on the original $100, the bank charges it on the current $110: $110 × 10% = $11. Add that on and Derek owes $110 + $11 = $121, a dollar more than the $120 from simple interest. That extra dollar is interest earned on interest, and given enough time it dwarfs the original deposit.

How often interest compounds matters too. The more often it is added, the more you earn on the same rate, because each new bit of interest starts earning right away. The graph below tracks a $1,000 investment at 20% for 40 years at three frequencies. The lines sit almost on top of each other early on, then fan out as the years stack up.

Continuous compounding, the mathematical limit where interest is added at every instant, always finishes highest. For most accounts the practical difference between daily and continuous is tiny, but annual clearly trails the rest. The Compound Interest Calculator lets you test frequencies side by side.

The rule of 72

There is a quick trick for compound interest you can do without a calculator. Divide 72 by the interest rate and you get the rough number of years it takes to double your money. At 8%, that is 72 ÷ 8 = 9 years for $1,000 to reach $2,000. It is an estimate, not a precise answer, and it holds up best for rates between 6% and 10%, though it stays close enough for anything under about 20%.

Fixed vs. floating rate

A rate on a loan or a savings account is either fixed or floating. A fixed rate stays put for the whole term, which is what this calculator assumes. A floating rate rides on top of a reference rate, such as the U.S. federal funds rate. Loan rates sit a little above the reference and savings rates a little below, and the bank keeps the spread. The federal funds rate is the main lever the Federal Reserve uses to steer the money supply, so a floating rate moves with policy and general conditions rather than holding a promised number.

Contributions

The calculator lets you add money on a schedule, which fits anyone who saves a set amount each month or year. One detail changes the result more than it looks: whether each deposit lands at the beginning or the end of a compounding period. A deposit made at the beginning earns interest for that whole period; the same deposit made at the end sits idle until the next one, so it collects one fewer period of interest over the life of the plan. Over decades that timing adds up.

Tax rate

Some interest income gets taxed. Corporate bonds, most savings interest, and certificates of deposit are usually taxable, while interest on U.S. federal treasury bonds is taxed federally but generally exempt from state and local tax. The bite is larger than people expect, because tax comes out every compounding period, not once at the end. Say Derek saves $100 at 6% for 20 years. Tax-free, $100 × (1 + 6%)^20 = $320.71. Put him in a 25% marginal bracket and he ends with $239.78, roughly a quarter of the growth gone.

Inflation rate

Inflation is the steady rise in prices over time, and it means a fixed pile of cash buys less next year than it does today. U.S. inflation has averaged around 3% over the past century, against roughly 10% a year for the S&P 500 across the same stretch. Leave the inflation field at 0 for a quick nominal figure. Fill it in and the calculator also reports the buying power of your ending balance in today's dollars. Tax and inflation together are a real drag: with a 25% tax rate and 3% inflation, you need to earn about 4% just to keep the real value of your money flat, and clearing that bar is harder than it sounds. Once you are comparing growth, our Savings Calculator and Investment Calculator take the same math further.

Rate against yield, and why the two differ

A quoted rate and what you actually earn are different numbers whenever interest compounds more often than once a year. The annual percentage yield folds the compounding in, which is why banks are required to advertise savings in APY under the Truth in Savings Act. Take a 5% nominal rate: compounded quarterly it yields 5.0945%, monthly 5.1162%, daily 5.1267%, and continuously 5.1271%.

Two things follow. Comparing a rate against a yield understates the account quoting the rate, so compare like against like. And the gains from compounding more often run out quickly, since the whole distance from daily to continuous compounding is four ten-thousandths of a percent. A tenth of a point of extra rate beats any change of compounding frequency.

The rule of 72, and where it drifts

Dividing 72 by the rate gives a close estimate of the years to double. It is closest around 8% and drifts at the extremes. At 3% the rule says 24 years and the exact answer is 23.4. At 10% the rule says 7.2 years and the exact answer is 7.3. The exact form is the natural log of 2 divided by the natural log of one plus the rate, which is what this calculator uses.

Tax, and the return that survives it

Interest from a savings account, a CD or a money market account is taxed as ordinary income at your marginal rate, in the year it is credited rather than the year you withdraw it. Banks report it on Form 1099-INT once it reaches $10 for the year, and interest below that threshold is still taxable even though no form arrives.

The practical effect is that a headline yield is not what you keep. At a 24% marginal rate, a 5% yield is 3.8% after federal tax, before any state tax. Compare that with inflation and the real return can be close to nothing, which is the case for holding a large balance in cash for years rather than for months.

Where the money is safe

Federal deposit insurance covers $250,000 per depositor, per insured bank, for each ownership category. The categories are the part people miss: single accounts, joint accounts and certain retirement accounts are insured separately, so a couple can hold considerably more than $250,000 at one bank and stay fully covered. Balances above the limit at a single institution are not insured, and splitting them across banks costs nothing.