UtilsKit
Global English

Compound Interest Calculator

Enter a starting amount, what you add each month, a yearly rate and how often interest is compounded to see the balance year by year and how much of it is interest.

The currency menu changes only the symbol and format; amounts are not converted.

$

Balance after 20 years

$109,333.14

Total interest earned
$51,333.14
Money you put in
$58,000.00
Added each compounding period
$200.00 × 12 a year

$10,000.00 plus $200.00 a month at 5% compounded monthly grows to $109,333.14 in 20 years, of which $51,333.14 is interest.

Your numbers

i = 5% ÷ 12 = 0.00416667

C = $200.00 × 12 ÷ 12 = $200.00 per period

n = 20 × 12 = 240 periods

FV = P(1+i)^n + C((1+i)^n − 1) ÷ i = $109,333.14

interest = FV − money added = $51,333.14

How compound interest is calculated
Balance at the end of each year

Year-by-year growth

20 years · amounts at each year end

Year Added Interest Total put in Balance
1$2,400.00$567.39$12,400.00$12,967.39
2$2,400.00$719.21$14,800.00$16,086.60
3$2,400.00$878.79$17,200.00$19,365.39
4$2,400.00$1,046.54$19,600.00$22,811.93
5$2,400.00$1,222.87$22,000.00$26,434.80
6$2,400.00$1,408.23$24,400.00$30,243.03
7$2,400.00$1,603.06$26,800.00$34,246.09
8$2,400.00$1,807.87$29,200.00$38,453.96
9$2,400.00$2,023.15$31,600.00$42,877.11
10$2,400.00$2,249.44$34,000.00$47,526.55
11$2,400.00$2,487.32$36,400.00$52,413.87
12$2,400.00$2,737.36$38,800.00$57,551.23
13$2,400.00$3,000.21$41,200.00$62,951.44
14$2,400.00$3,276.48$43,600.00$68,627.92
15$2,400.00$3,566.91$46,000.00$74,594.83
16$2,400.00$3,872.18$48,400.00$80,867.01
17$2,400.00$4,193.08$50,800.00$87,460.09
18$2,400.00$4,530.40$53,200.00$94,390.49
19$2,400.00$4,884.97$55,600.00$101,675.46
20$2,400.00$5,257.68$58,000.00$109,333.14

How compound interest is calculated

Simple interest is paid on the original amount only. Compound interest is paid on the balance, and the balance includes the interest already credited, so each period's interest is slightly larger than the last. How often interest is credited, the compounding frequency, decides how many times a year that happens: once a year, twice, four times, twelve times or every day.

  • i = r ÷ k: the rate per period, where r is the yearly rate you enter and k is the number of compounding periods a year (1, 2, 4, 12 or 365).
  • C = M × 12 ÷ k: your monthly contribution M spread over the compounding periods. With monthly compounding it is simply M.
  • n = t × k: the number of periods in t years.
  • FV = P(1 + i)ⁿ + C((1 + i)ⁿ − 1) ÷ i: the balance after n periods, starting from P. At a 0% rate it is just everything you put in.

The calculator works through it one period at a time: interest on the balance at the start of the period, then the period's contribution added at its end. A contribution therefore earns nothing in the period it is made. With yearly compounding, a year of monthly contributions is added at the end of the year and starts earning from the next one; with monthly compounding each contribution starts earning the following month. This is the same convention the SEC's Investor.gov Compound Interest Calculator uses, and it gives the same results to the cent for all five frequencies: with the inputs of the second example below, $96,993.25 annually, $98,672.24 semiannually, $99,542.02 quarterly, $100,133.64 monthly, $100,423.18 daily.

Amounts are not rounded along the way; each year-end balance is rounded to the cent, and the interest column is that balance minus the money put in, so the columns of the schedule always add up. The rate stays the same for the whole period and nothing is taken out for taxes, fees or inflation.

Worked examples from official sources

The CFPB's $1,000 at 5%

The Consumer Financial Protection Bureau explains compound interest with $1,000.00 at 5% compounded once a year. In the first year it earns $50.00, for a balance of $1,050.00. In the second year the 5% is paid on $1,050.00, which is $52.50, for a balance of $1,102.50. The extra $2.50 in year two is interest on the first year's interest. These are the figures the CFPB publishes.

Investor.gov: $10,000.00 plus $500.00 a month

Entering $10,000.00, a monthly contribution of $500.00, 10 years, 6% and monthly compounding in the Investor.gov calculator returns $100,133.64. Step by step:

  1. Rate per month: 6% ÷ 12 = 0.005, over 120 months.
  2. The starting $10,000.00 on its own grows to $18,193.97.
  3. The 120 contributions of $500.00 add $60,000.00 of your money and grow to $81,939.67.
  4. Together: $100,133.64, of which $30,133.64 is interest, the same amount Investor.gov returns. With yearly compounding the same inputs give $96,993.25, because each year's contributions start earning only at the end of the year.

How time, rate, contributions and frequency change the result

The calculator opens with $10,000.00, $200.00 a month, 5% and monthly compounding over 20 years: $109,333.14, of which $51,333.14 is interest. These are starting values to edit, not an expected rate of return. Halfway, after 10 years, the balance is $47,526.55.

Time

  • 10 years: $47,526.55, with $13,526.55 of interest on $34,000.00 put in.
  • 20 years: $109,333.14, with $51,333.14 of interest on $58,000.00 put in.
  • 30 years: $211,129.17, with $129,129.17 of interest on $82,000.00 put in.
  • 40 years: $378,788.20, with $272,788.20 of interest on $106,000.00 put in.

Interest in the first year is $567.39; in year 20 it is $5,257.68, because it is paid on everything that has built up.

Rate

  • 3%: $83,867.95 after 20 years.
  • 5%: $109,333.14 after 20 years.
  • 7%: $144,572.72 after 20 years.

A savings account or certificate of deposit pays a stated rate. Investments such as stocks and funds have no fixed rate: their value moves every year and can fall, so a single rate in this calculator is only an assumption that you choose.

Starting amount and monthly contributions

The starting $10,000.00 alone grows to $27,126.40. The $200.00 a month alone, with nothing at the start, grows to $82,206.73. The two parts grow independently, so together they make up the combined $109,333.14, give or take a cent of rounding.

Compounding frequency

  • Annually: $105,891.27.
  • Semiannually: $107,733.70.
  • Quarterly: $108,686.13.
  • Monthly: $109,333.14.
  • Daily: $109,649.55.

More frequent compounding ends a little higher, but the gap between monthly and daily is small next to the effect of the rate, the time or the amount you put in.

Frequently asked questions

What is the difference between the interest rate and the APY?

The rate is the yearly figure before compounding; the annual percentage yield (APY) is what a year of compounding actually earns. $1,000.00 at 6% compounded monthly earns $61.68 in a year, an APY of 6.17%; Regulation DD, the U.S. Truth in Savings rule, uses the same $61.68 on $1,000.00 as its example of a 6.17% APY. At 6% the APY is 6.00% with yearly compounding and 6.18% with daily compounding. If your bank quotes an APY, enter it with yearly compounding.

How long does it take to double my money?

At 5% compounded yearly with no contributions, a balance doubles in about 14.2 years. The rule of 72, dividing 72 by the rate, estimates 14.4 years. The rule is a mental shortcut; the calculator uses the exact formula.

What if I contribute at the start of each month?

The calculator adds contributions at the end of each compounding period, as the Investor.gov calculator does. Money added at the start of a month would earn one more month of interest each time, so the true result is slightly higher. Contributions made on a different schedule, such as once a year, can be entered as the monthly equivalent for an estimate.

Are taxes, fees and inflation included?

No. The result is the balance before any tax on interest or gains, any account or fund fees and any loss of purchasing power. To see the effect of a yearly fee on an investment, enter the rate minus the fee; to see a balance in today's money, enter the rate minus the inflation rate you want to assume.

Can I use it for a debt?

It shows how an unpaid balance grows when interest is added to it, but repaying a loan or a credit card works the other way round, with payments reducing the balance.

Sources