Compound interest calculator
How a balance grows with compounding and regular deposits, year by year.
Result
- Final balance
- $47,526.55
- Initial deposit
- $10,000.00
- Total contributions
- $24,000.00
- Interest earned
- $13,526.55
- Interest share of balance
- 28.5%
- Effective annual yield (APY)
- 5.1162%
Year-by-year growth
| Year | Deposits to date | Interest that year | Interest to date | Balance |
|---|---|---|---|---|
| 1 | $12,400.00 | $567.39 | $567.39 | $12,967.39 |
| 2 | $14,800.00 | $719.21 | $1,286.60 | $16,086.60 |
| 3 | $17,200.00 | $878.79 | $2,165.39 | $19,365.39 |
| 4 | $19,600.00 | $1,046.54 | $3,211.93 | $22,811.93 |
| 5 | $22,000.00 | $1,222.87 | $4,434.80 | $26,434.80 |
| 6 | $24,400.00 | $1,408.23 | $5,843.03 | $30,243.03 |
| 7 | $26,800.00 | $1,603.06 | $7,446.09 | $34,246.09 |
| 8 | $29,200.00 | $1,807.87 | $9,253.96 | $38,453.96 |
| 9 | $31,600.00 | $2,023.15 | $11,277.11 | $42,877.11 |
| 10 | $34,000.00 | $2,249.45 | $13,526.55 | $47,526.55 |
How this was calculated
Growth of the initial deposit
A = P × (1 + r/n)^(n × t)
$10,000.00 × (1 + 0.05/12)^(12 × 10) = $16,470.09
Rate per contribution period
i = r / n
i = 0.416667% per month
Value of 120 contributions
FV = PMT × ((1 + i)^N − 1) / i
$200.00 × ((1 + 0.00416667)^120 − 1) / 0.00416667 = $31,056.46
Final balance
Deposit growth + contribution value
$47,526.55
Effective annual yield
APY = (1 + r/n)^n − 1
5.1162%
What this calculation assumes
- The rate stays the same for the whole term and is a nominal annual rate compounded at the frequency you chose.
- Contributions earn at the same effective rate as the balance, even when they are made more or less often than interest compounds.
- Each contribution is made at the end of its period, so the first one earns nothing until the next period.
- No taxes, fees, withdrawals or inflation are deducted. Investment returns are not guaranteed and can be negative.
Estimates for information only. They are not financial advice, a loan offer or a guarantee of any return, rate or approval. Lenders and providers calculate with their own terms; check yours before you decide.
How compounding works
Compound interest is interest earned on interest. Each time interest is credited it joins the balance, and the next period's interest is calculated on the larger amount. The more often it compounds, the slightly faster the balance grows; the effective annual yield (APY) shows the difference.
The formulas
A = P × (1 + r/n)^(n × t)
P is the starting deposit, r the annual rate, n the number of compounding periods a year and t the number of years. Continuous compounding uses A = P × e^(r × t).
Regular deposits are added with the future value of an annuity, FV = PMT × ((1 + i)^N − 1) ÷ i, where i is the rate per deposit period and N the number of deposits. When deposits and compounding happen at different frequencies (monthly deposits, daily compounding), i is the equivalent rate per deposit period, (1 + r/n)^(n/q) − 1, so every deposit grows at exactly the same effective rate as the balance.
Example: $10,000 at 5% compounded monthly for 10 years grows to $16,470.09. Adding $200 at the end of every month adds $31,056.46 more, for $47,526.55.
Start or end of the period
Deposits made at the start of each period earn one extra period of interest compared with deposits at the end. Many savings plans take money at the start of the month; loans and most annuity examples assume the end. The result changes noticeably over long terms, so choose the one that matches your plan.
Questions people ask
What is the rule of 72?
Divide 72 by the annual rate to estimate how many years it takes to double: at 6%, about 12 years. It is an approximation; this calculator gives the exact figure.
What is the difference between APR and APY?
APR is the nominal yearly rate. APY includes the effect of compounding within the year. 6% compounded monthly is an APY of 6.168%.
Are investment returns compound interest?
Reinvested returns compound in the same way, but they are not fixed: markets go up and down. Treat a rate for investments as an assumption, not a promise.