Finance
Compound Interest Calculator
Project savings and investment growth with regular contributions and compounding.
Result
Enter your numbers and press Calculate to see the result.
Calculating…
How compound interest is calculated
Compound interest pays you interest on your interest. Each period, the balance earns a return, and that return is added back so the next period's interest is calculated on a larger amount. Over time this snowball effect makes the balance grow far faster than simple interest, which only ever pays on your original deposit. This calculator adds your monthly contribution to the balance as it goes, so contributions and compounding work together.
Formula
A = P(1 + r/m)^(m·t) + PMT × [((1 + i)ⁿ − 1) ÷ i]
where P is the starting amount, r the annual rate, m the number of compounding periods per year, t the number of years, PMT the recurring contribution, i the periodic rate, and n the number of contribution periods. The first term grows your initial deposit; the second grows the stream of contributions.
Worked example
$10,000 starting balance, $300 added monthly, 7% annual return, compounded monthly for 20 years:
- Total contributions: $10,000 + ($300 × 240) = $82,000
- Final balance: ≈ $196,000
- Interest earned: ≈ $114,000 — more than the money you put in.
The longer the money stays invested, the larger the interest slice becomes. Starting five years earlier often beats contributing more later, because those early deposits have the most time to compound.
Compounding frequency
Interest can be added daily, monthly, quarterly, or annually. More frequent compounding earns a little more at the same headline rate, because interest starts earning its own interest sooner. The gap is usually small — the interest rate and the length of time you stay invested matter far more than how often it compounds.
Ways to grow the balance faster
- Start early — time is the most powerful input; every extra year compounds on everything before it.
- Contribute regularly — steady monthly deposits raise the balance that earns interest.
- Reinvest returns — leaving interest and dividends in the account is what makes compounding work.
- Mind the rate — a higher return compounds faster, but higher returns usually carry more risk.
Every compound interest formula in one place
| What you need | Formula |
|---|---|
| Final amount | A = P(1 + r/n)^(nt) |
| Interest earned only | CI = A − P |
| With regular contributions | A = P(1 + i)^N + PMT × ((1 + i)^N − 1) ÷ i |
| Depreciation (compound decay) | A = P(1 − r)^t |
| Time to double | t ≈ 72 ÷ rate as a percentage |
P is the starting amount, r the annual rate as a decimal, n the compounding periods per year, t the years, and in the contributions formula i is the rate per period and N the total number of periods. Depreciation is the same equation with the sign flipped — a car losing 15% a year is compound interest running backwards.
Compounding frequency: monthly, half-yearly, daily
The stated rate is annual; n decides how often it is applied. More frequent compounding pays slightly more, with diminishing returns that stop mattering quickly.
| Frequency | n | $10,000 at 6% after 10 years |
|---|---|---|
| Annually | 1 | $17,908 |
| Half-yearly | 2 | $18,061 |
| Quarterly | 4 | $18,140 |
| Monthly | 12 | $18,194 |
| Daily | 365 | $18,220 |
The whole gap from annual to daily is $312 over a decade — about 1.7%. Frequency is worth understanding and rarely worth choosing a product over; the rate and the contributions dominate everything.
Worked examples over 2 and 3 years
Take $5,000 at 8% compounded annually:
| Year | Opening | Interest | Closing |
|---|---|---|---|
| 1 | $5,000.00 | $400.00 | $5,400.00 |
| 2 | $5,400.00 | $432.00 | $5,832.00 |
| 3 | $5,832.00 | $466.56 | $6,298.56 |
Simple interest would have paid $400 every year, for $6,200. The $98.56 difference after three years is the whole idea — and it is why the curve on the chart bends upward rather than running straight.
Compound interest in Excel and Google Sheets
| Goal | Formula |
|---|---|
| Final amount, no contributions | =A2*(1+B2/C2)^(C2*D2) |
| With regular contributions | =FV(rate/12, years*12, -payment, -principal) |
| Rate needed to reach a target | =RATE(periods, -payment, -principal, target) |
FV is the built-in future value function and it expects payments as negative numbers, because money
leaving your pocket is a negative cash flow. Omitting the minus signs returns a negative balance.
The same maths on debt
Compounding is direction-neutral. On a credit card at 22% APR compounded daily, an untouched $3,000 balance grows to about $3,738 in a year — the same equation that builds savings, working against you. This is why paying down high-interest debt usually beats investing the same money: the guaranteed 22% you stop paying is larger than the return you would expect to earn.
Dividend reinvestment behaves the same way in reverse: reinvested payouts buy more shares, which pay more dividends. That is compounding even though nobody calls it interest.
Paying off debt instead? The loan payment calculator applies the same compounding math in reverse to show what borrowing costs you.
Compound Interest Calculator — frequently asked questions
What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the compounding periods per year, and t the years. Interest earned alone is A minus P.
How much difference does monthly compounding make?
Less than most people expect. $10,000 at 6% over 10 years grows to $17,908 compounded annually and $18,194 monthly — about 1.6%. The rate and your contributions matter far more than the frequency.
How do I calculate compound interest in Excel?
For a lump sum use =A2*(1+B2/C2)^(C2*D2). With regular contributions use the built-in =FV(rate/12, years*12, -payment, -principal), entering payments as negative numbers.
What is the formula for half-yearly compound interest?
The same formula with n = 2, so A = P(1 + r/2)^(2t). The annual rate is halved and applied twice a year.
Does compound interest work on debt too?
Yes, identically. A $3,000 credit card balance at 22% APR compounded daily grows to about $3,738 in a year — which is why clearing high-interest debt usually beats investing the same money.
What is compound interest?
Compound interest is interest earned on both your original money and the interest it has already earned. Because each period builds on a larger balance, growth accelerates over time — unlike simple interest, which is only ever calculated on the starting amount.
How does compounding frequency affect the result?
More frequent compounding means interest is added to the balance more often, so it starts earning its own interest sooner. Daily compounding earns slightly more than annual compounding at the same rate, though the difference is small compared with the interest rate and the length of time you stay invested.
Do regular contributions really matter that much?
Yes. Adding a fixed amount every month steadily raises the balance that earns interest, so contributions and compounding reinforce each other. Over long periods, consistent monthly deposits often add more to the final balance than the starting amount does.
What interest rate should I use?
Use a rate that matches your account or investment: a savings account might return 2–5%, while a diversified stock-market portfolio has historically averaged roughly 7% a year after inflation. The rate is an assumption — real returns vary, so try a few values to see a range of outcomes.