Interest Calculator

What the interest calculator works out

Interest questions run in one of two directions. You know the balance, the rate and the term, and you want the interest. Or you know what the balance has to become, and you need the rate that gets you there. This page handles both: the mode selector switches between them, and the same compounding setting applies to either answer.

In interest mode you enter a starting amount, an annual rate, a term in years, and how often interest is added. The result is the compound balance, the interest earned, the simple interest on the same terms, and the gap between the two. That gap is the part of the return that comes from interest earning interest, and it grows faster than the headline rate suggests.

In rate mode the target amount takes the place of the rate. The calculator solves for the annual rate that turns the starting amount into the target over the term, at the compounding frequency you pick. It also shows the simple interest rate that would reach the same target, which is always higher because simple interest never compounds.

Both modes are lump sum math. There are no monthly deposits here, no fees, and no taxes in the headline number. The sections below explain what each figure means, where the formulas come from, and what the answer leaves out.

Simple interest: the flat charge

Simple interest is paid on the original principal only. The interest never joins the balance, so the annual payment stays the same for the whole term. The formula is I = P x r x t, with the rate written as a decimal.

Put in the numbers from the top of this page: $10,000 x 0.05 x 10 = $5,000. The balance after ten years is $15,000, and each of those ten years earned $500, not a cent more. The arithmetic is linear, so doubling the term doubles the interest and halving the rate halves it.

Simple interest shows up in car loans quoted on a precomputed basis, in some short term business notes, and in the classroom version of the interest lesson. It also appears in interest only loans, where the payment covers the interest and the principal never moves. For anything that stays invested and lets the interest sit, simple interest understates what happens next.

That understatement is the useful part. Running the simple version next to the compound version on the same principal and rate shows what compounding is worth in dollars, without any change to the rate itself.

Compound interest: interest on the interest

Compound interest adds each period's interest to the balance, so the next period earns on a larger amount. The formula is A = P(1 + r/n)^(nt), where n is the number of compounding periods in a year and t is the term in years.

For $10,000 at 5 percent for 10 years with monthly compounding: 10,000 x (1 + 0.05/12)^120 = 16,470.09. The exponent is 120 because 12 periods a year run for 10 years. The monthly rate is 0.05/12 = 0.0041667, a small number applied 120 times.

The first year pays $511.62, not $500. The extra $11.62 is interest on the interest that built up during the year. By year ten the balance is growing at about $800 a year, because 5 percent of $16,000 is a bigger number than 5 percent of $10,000. Nothing about the rate changed; only the base it applies to changed.

That is why the compound curve looks flat at the start and steep at the end. The early years are dominated by the principal, and the later years are dominated by the accumulated interest.

Compounding frequency moves the yield, not the rate

The quoted annual rate stays at 5 percent no matter how often interest is added. What changes is the effective annual yield, the APY, which is the actual percentage gained over one year after the intra-year compounding is counted.

The spread is small at these rates: 5.0000 percent once a year against 5.1267 percent daily, or about $12.67 a year on $10,000. On a $250,000 balance the same difference is roughly $317 a year, which is why banks quote APY rather than the nominal rate on deposit products.

Continuous compounding is the mathematical limit, with interest added at every instant. It uses e^(rt) instead of (1 + r/n)^(nt), and at 5 percent it lands at 5.1271 percent, which is 0.0004 percentage points above daily compounding. Past daily, the extra frequency stops mattering in any practical sense.

Running it backward: the rate a target needs

Rate mode answers a different question: what annual rate turns today's balance into a stated target over a stated term. The formula is rearranged from the compound one, r = n x ((A/P)^(1/(nt)) - 1).

To turn $10,000 into $20,000 in 10 years with monthly compounding, the rate is 12 x ((2)^(1/120) - 1) = 0.0695, or 6.95 percent a year. The same target on simple interest needs 10 percent, because simple interest never earns on itself. That 3 point gap is the value of compounding over a decade.

Term length does most of the work. The table shows the rate needed to double a balance at several horizons, all with monthly compounding.

Two things follow from that table. A short horizon demands a rate that most safe savings accounts will not pay, so the target has to move or the term has to stretch. A long horizon asks for a rate that is close to what a diversified portfolio has returned over decades, which is why time is the lever people control.

The rate this mode returns assumes one deposit and no withdrawals. Add monthly deposits and the required rate falls, because the deposits carry part of the load.

Worked example: $10,000 at 5 percent for 10 years

Here is the whole path year by year, with monthly compounding and no deposits. The middle column is the balance at the end of each year, and the right column is the interest accumulated since the start.

Check the last row against the formula: 10,000 x 1.0041667^120 = 16,470.09. The simple version of the same deal pays 10,000 x 0.05 x 10 = 5,000, so compounding adds 1,470.09, which is 29 percent more interest on an unchanged rate.

Notice the shape of the interest column. It reaches $511.62 in year one, $2,833.59 by year five, and $6,470.09 by year ten. Each five year block adds more than the one before it: the first block adds $2,833.59, the second adds $3,636.50. The balance is doing the work in the second half.

Tax and inflation take a share

Interest is ordinary income in the United States, taxed in the year it is credited, even if you leave it in the account. At a 24 percent marginal rate the $6,470.09 of compound interest carries about $1,552.82 of federal tax, leaving $4,917.27. The simple interest case is taxed the same way on its smaller base.

Inflation is the second deduction, and it does not appear on any statement. At 2.5 percent a year, $16,470.09 in ten years buys what $12,866.41 buys today. The nominal gain looks like 64.7 percent; the real gain is 28.7 percent. On the simple interest side the real gain is 17.2 percent.

Tax deferred accounts change the first line and not the second. Interest inside an IRA or a 401(k) is not taxed as it accrues, so the full balance keeps compounding, but withdrawals are taxed later and inflation still applies.

Comparing two offers without guessing

Two accounts that quote 5.00 percent and 5.12 percent look close. Over ten years on $10,000 the difference is small, but the same comparison on a rate that is one full point higher is not: $10,000 at 6 percent for ten years reaches $18,193.97, which is $1,723.88 more than the 5 percent case.

Use APY when the products are savings accounts or certificates of deposit, because APY already includes the compounding. Use APR when the product is a loan, and read the note rate and the fees separately, since APR folds fees into a single number that hides the cost of the money itself.

Check who stands behind the balance. Deposits at a US bank are insured to $250,000 per depositor, per bank, per ownership category by the FDIC, and Treasury securities bought at TreasuryDirect carry the full faith of the federal government. The SEC's investor education site has a parallel calculator that is useful for a second opinion on the compounding math.

One caution on promotional rates: a 5 percent teaser that drops to 1 percent after six months is not a 5 percent account. Run the rate you expect to hold, not the rate on the banner, and the answer will be closer to what the statement shows next year.