Compound Interest Calculator

FV = P × (1 + r ÷ m)^(m × t), and for continuous compounding FV = P × e^(r × t)

P

The amount you start with

r

The nominal annual interest rate, as a decimal rather than a percentage

m

How many times a year the interest is added — 1, 2, 4, 12 or 365

t

The number of whole years the money is left alone

FV

The balance at the end, which is also called the future value

Use it whenever a rate is quoted with a compounding frequency attached and you want the actual number rather than the quoted one. The formula above is the only one you need; the frequency field changes one exponent and nothing else. It is worth running twice at two different frequencies before you commit money, because the gap between annual and monthly is real and grows with the rate and the term — at 5% over ten years it is 181.14, and at higher rates over longer terms it is thousands. The single most useful comparison on this page is the last two outputs read together: the interest earned with compounding against the interest the same money would have earned without it.

1. 10,000 at 5% for ten years, compounded monthly

   1. Periodic rate: 5 ÷ 100 ÷ 12 = 0.00416667 a month
   2. Periods: 12 × 10 = 120 months
   3. Balance: 10,000 × 1.00416667^120 = 16,470.09
   4. Interest earned: 16,470.09 − 10,000 = 6,470.09
   5. Effective annual rate: 1.00416667^12 − 1 = 5.116%
   6. Simple interest for the same ten years: 10,000 × 5% × 10 = 5,000.00, so compounding adds 6,470.09 − 5,000.00 = 1,470.09

   This is the page's default. Read the last two outputs as a pair: compounding is worth 1,470.09 here, and that number is invisible on a page that only quotes the rate.

2. 100,000 at 4.5% for thirty years, compounded monthly

   1. Periodic rate: 4.5 ÷ 100 ÷ 12 = 0.00375 a month
   2. Periods: 12 × 30 = 360 months
   3. Balance: 100,000 × 1.00375^360 = 384,769.80
   4. Interest earned: 384,769.80 − 100,000 = 284,769.80
   5. Effective annual rate: 1.00375^12 − 1 = 4.594%
   6. Simple interest: 100,000 × 4.5% × 30 = 135,000.00, so compounding adds 149,769.80

   Compare this with the example above: the money is ten times larger and the term three times longer, but the balance is twenty-three times larger. Compounding is not a straight line, and most of the curvature sits in the later years.

3. 10,000 at 5% for ten years, compounded continuously

   1. Continuous growth: 10,000 × e^(0.05 × 10) = 10,000 × e^0.5 = 16,487.21
   2. Interest earned: 16,487.21 − 10,000 = 6,487.21
   3. Effective annual rate: e^0.05 − 1 = 5.127%
   4. Simple interest for the same ten years: 5,000.00, so compounding adds 1,487.21

   Continuous compounding is the ceiling, not a product: it beats 16,486.65 at daily compounding by 0.56, and no discrete frequency can ever overtake it. Reading the frequency table downwards, that is what the last row is doing.

This page prices one lump sum left untouched, and that is the whole of it. It does not model anything added later — no monthly deposits, no withdrawals, no contributions that rise with inflation — so a savings plan where you pay in every month needs the investment calculator rather than this one. It also assumes the rate holds for the whole term. Real savings rates move: a promotional rate expires, a central bank cuts, a fixed-rate bond matures and has to be reinvested at whatever is on offer then, and the answer here is a projection made with today's rate rather than a promise. Tax is not in it, and for most savers tax is taken out of the interest as it accrues, which means the balance you actually keep grows more slowly than this; a taxable account at a 30% marginal rate keeps roughly seven tenths of the interest shown. Inflation is absent too, so 16,470.09 in ten years buys less than 16,470.09 today. Nothing here is rounded along the way, which makes the arithmetic exact but means it can differ by a cent or two from an account statement where the bank rounds each posting. Finally, the amounts carry no currency symbol — they are right in whatever currency you had in mind and wrong in any other.

How do I work out compound interest on a lump sum?

Take the amount, multiply it by one plus the periodic rate raised to the number of periods, where the periodic rate is the annual rate divided by how many times a year interest is added and the number of periods is that same number times the years. 10,000 at 5% compounded monthly for ten years is 10,000 × 1.00416667^120 = 16,470.09. That works out at 6,470.09 of interest earned. This is the compound interest formula in its only form — everything else on the page is that formula read at a different frequency.

What is the difference between the annual rate and the effective annual rate?

The annual rate — 5% in the example on this page — is the quoted rate. The effective annual rate is what the money actually grows by in a year once the interest within that year has itself earned interest: 5.116% at monthly compounding, 5.127% at continuous compounding, and exactly 5.000% if interest is added only once a year. The two are equal only at annual compounding, and the gap between them widens with the frequency and the rate.

Which compounding frequency should I choose?

The one your account actually uses, which is usually stated in the terms. If you are comparing products, compare their effective annual rates rather than their quoted rates, because those are already on the same footing. Frequency works in your favour as a saver and against you as a borrower, and it is worth knowing how much it moves: on 10,000 at 5% over ten years the spread from annual to daily compounding is 197.70.

Is continuous compounding real, or just a mathematical idea?

Both. No savings account adds interest every instant, so as a product it does not exist — but as a limit it is exactly what textbooks, option pricing and a great deal of central bank arithmetic use, and it is the number every discrete frequency approaches as it gets finer. Monthly gets 16,470.09, daily 16,486.65, continuous 16,487.21 on the same 10,000. It is offered here so you can see the ceiling.

Does compounding frequency matter more than the rate?

No, and it is not close. Moving 10,000 from 5% to 6% over ten years at monthly compounding is worth 1,723.88 more, while going from annual to continuous compounding at 5% is worth 198.26. One percentage point of rate beats every frequency choice available, and both are dwarfed by adding years. Frequency is a real effect and it is free to get right, but the rate and the term dominate it. Change the rate first, then the term, then the frequency.

Why does this page not include tax or inflation?

Because both depend on facts the page cannot know. Tax on interest depends on your bracket, your country and whether the account is tax-sheltered, and inflation depends on which index and which period you mean. A balance built at 5% is a nominal balance — the money you will see — and a real return subtracts whatever inflation did over the same years. Treat the number here as the nominal one and adjust it yourself for the two.

• Compound Interest Calculator — the same closed form, with the frequency explained — U.S. Securities and Exchange Commission (Investor.gov)
• 12 CFR Part 1026, Appendix J — the periods-per-year convention behind every frequency on this page — Electronic Code of Federal Regulations (United States)
• H.15 Selected Interest Rates — the published rates an annual rate field stands in for — Board of Governors of the Federal Reserve System (United States)