How compound interest grows
With compounding, interest is added to the balance at the end of each period and then earns interest itself. The more often it compounds and the longer it runs, the larger the gap from simple interest. The annual rate divided by the number of periods gives the periodic rate; the effective annual yield, or APY, is what one year of compounding actually returns.
Worked example (pre-filled). $5,000 at 4.5% compounded monthly for 10 years, with $200 added at the end of every month, grows to $38,074.58. Of that, $29,000.00 was put in and $9,074.58 is interest. Monthly compounding at 4.5% is an APY of 4.594%.
The table shows the balance at each year end. Contributions dominate early; interest overtakes them later, which is the point of starting early. The calculator ignores taxes on interest, fees and inflation, and assumes the rate never changes, so it is an arithmetic illustration rather than a forecast. This page computes; it does not recommend a loan, lender, investment or tax position. The savings goal calculator works the other way round: it finds the monthly deposit that reaches a target.
Formula and assumptions
monthly deposits: i = (1 + r ÷ n)n ÷ 12 − 1; balance = PMT × ((1 + i)12t − 1) ÷ i
APY = (1 + r ÷ n)n − 1
- Deposits are made at the end of each month and earn the same effective rate as the lump sum.
- No withdrawals, taxes, fees or rate changes.
Frequently asked questions
What is $5,000 at 4.5% compounded monthly for 10 years?
$7,834.96 with no further deposits. Adding $200 a month brings it to $38,074.58, of which $9,074.58 is interest.
What is the compound interest formula?
A = P × (1 + r/n)^(n×t): principal P, annual rate r, n compounding periods a year, t years.
Does daily compounding make a big difference?
Small at typical rates. 4.5% compounded monthly is a 4.594% APY; daily is 4.602%.
What is APY?
Annual percentage yield: the interest actually earned in a year including compounding, (1 + r/n)^n − 1.
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Sources
This calculator gives general estimates from the figures you enter. It is not tax, legal, payroll or financial advice. See our disclaimer.