Compound interest calculator
Compounding is exponential, and the exponent is computed here as an exact rational power rather than a float, so a 40-year daily-compounded figure is right to the cent.
- Total you put in
- 70 000.00
- Interest earned
- 100 619.05
- Multiple of what you deposited
- 2.437
- Effective annual rate
- 7.2290 %
- Growth of the starting amount alone
- 40 387.39
- Growth of the contributions alone
- 130 231.66
Show the working
- Starting amount = 10 000
- Added each period = 250
- Annual interest rate = 7
- Years = 20
- Compounding and contribution frequency = 12
- i = 7 / 100 / 12 = 0.005 833 33
- n = 20 * 12 = 240
- growth = (1 + 0.005 833 33)^240 = 4.038 74
- Growth of the starting amount alone = 10 000 * 4.038 74 = 40 387.4
- Growth of the contributions alone = 0.005 833 33 == 0 ? 250 * 240 : 250 * (4.038 74 - 1) / 0.005 833 33 = 130 232
- Final balance = 40 387.4 + 130 232 = 170 619
- Total you put in = 10 000 + 250 * 240 = 70 000
- Interest earned = 170 619 - 70 000 = 100 619
- Multiple of what you deposited = 70 000 > 0 ? 170 619 / 70 000 : 0 = 2.437 42
- Effective annual rate = ((1 + 0.005 833 33)^12 - 1) * 100 = 7.229 01
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- A = P (1+i)^n + C ((1+i)^n - 1) / i
- i = annual rate / periods per year, n = years x periods per year
- Contributions are assumed to arrive at the end of each period.
Contributions at the start of each period earn one extra period of interest; the difference is small but real.
Nothing here accounts for inflation, tax or fees, all of which are larger than the compounding frequency effect.
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.
Frequently asked
What is the difference between APR and APY?
APR is the nominal rate ignoring compounding within the year. APY is what you actually earn once compounding is included: APY = (1 + APR/n)^n - 1.
How long does it take to double my money?
Divide 72 by the annual percentage rate for a quick estimate. At 7% that is about 10.3 years, against an exact 10.24.