How this compound interest calculator works
Put money in an account that pays interest and, at the end of the first period, you have your deposit plus a little interest. In the second period the interest is calculated on that slightly larger balance, so it is slightly larger too. Repeat for years and the small differences stack into a curve that bends upward. That is compounding, and it is why time in the market matters so much more than most people expect.
At a glance
- Interest earned in one period earns interest itself in the next.
- Regular deposits usually contribute more to the final balance than the starting lump sum.
- Compare accounts by APY, which already includes the compounding schedule.
- Time and rate matter far more than the compounding frequency.
The calculator takes a starting amount, an optional regular deposit, the interest rate, how often interest is credited and the number of years. It projects the balance month by month and reports the final figure, how much of it you paid in, how much is interest, and the effective annual rate (APY) that the compounding schedule produces. The chart and table underneath show the same projection year by year so you can see when interest overtakes deposits.
The formula
FV = P × (1 + r)^n
FV = P × (1 + r)^n + c × [((1 + r)^n − 1) ÷ r]
The first term grows the starting amount. The second grows a stream of equal deposits, each one compounds for a different length of time, and the bracket adds them all up. When deposits are made at the start of each period rather than the end, the second term is multiplied by (1 + r) because every deposit earns one extra period of interest.
When the deposit schedule and the compounding schedule differ, daily compounding with monthly deposits, say, there is no single r that fits both, so the calculator converts the compounding rate into an equivalent monthly growth rate and steps through the projection a month at a time. Whenever the two schedules match, that stepping reproduces the formula exactly.
Worked example: the default inputs
Start with $10,000, add $100 at the end of every month, earn 6% compounded monthly for 20 years.
Monthly rate: 6% ÷ 12 = 0.5%. Periods: 240.
Lump sum: 10,000 × 1.005240 = 10,000 × 3.3102 = $33,102.04.
Deposits: 100 × (3.3102 − 1) ÷ 0.005 = 100 × 462.04 = $46,204.09.
Final balance: $79,306.13. You paid in $34,000; the other $45,306 is interest, more than you contributed.
Nominal rate versus APY
A bank advertising "6% compounded monthly" is quoting a nominal rate. Because each month's interest earns interest for the rest of the year, you actually receive 6.168% over a full year. That figure is the annual percentage yield, shown beside the result.
APY = (1 + r ÷ m)^m − 1
The table below shows how little the compounding schedule moves the needle at 6%:
| Compounding | Periods per year | APY |
|---|---|---|
| Yearly | 1 | 6.000% |
| Half-yearly | 2 | 6.090% |
| Quarterly | 4 | 6.136% |
| Monthly | 12 | 6.168% |
| Daily | 365 | 6.183% |
| Continuous | ∞ | 6.184% |
Two lessons follow. First, when comparing accounts, compare APYs, not nominal rates, the APY already contains the compounding schedule. Second, the choice between monthly and daily compounding is worth a few dollars a year on a typical balance; a half-point difference in the rate itself is worth far more.
Why the deposits matter more than the lump sum
In the default example the $100 monthly deposits end up worth $46,204 while the $10,000 lump sum grows to $33,102. Over twenty years the steady stream of small deposits beats the larger initial amount, because $24,000 in total contributions is more money than $10,000, but also because each deposit still has years to compound.
Worked example: starting from nothing
Deposit $500 at the end of each month at 7% compounded monthly for 30 years, starting from $0.
Monthly rate 0.58333%, 360 periods. Growth factor 1.0058333360 = 8.1165.
FV = 500 × (8.1165 − 1) ÷ 0.0058333 = $609,985.50.
Total deposited: $180,000. Interest earned: $429,985. In the final year alone the balance grows by about $40,000, more than five years of deposits.
Reading the chart and table
The stacked chart separates three layers: the starting amount (flat, since it never changes), cumulative deposits (a straight ramp) and cumulative interest (the curve). The year in which the interest layer becomes the thickest is the point where the account is doing more work than you are.
The table gives the same information year by year. Start is the balance carried in, Deposits what you added during the year, Interest what the account credited and End balance the sum of the three. The rows always add up, and the last end balance is the headline figure.
What this calculator does not include
- Tax. Interest in an ordinary account is usually taxed every year, which slows compounding. In a tax-sheltered account the projection holds as shown.
- Inflation. A balance of $79,306 in twenty years will not buy what $79,306 buys today. Run the result through the inflation calculator, or use the retirement calculator, which shows real values.
- Changing rates. Savings rates move with central-bank policy. The projection assumes the rate you enter holds for the whole term, try a low and a high case to see the range.
- Fees. Account or fund fees reduce the effective rate. If you pay 0.5% a year in fees on a 7% return, enter 6.5%.
Using the result
Use the calculator to answer concrete questions: how much will I have if I keep this up, how much sooner do I reach a target if I add $50 a month, and what does a one-point rate difference cost over the long run. If you have a specific target in mind, the savings goal calculator inverts the same formula to tell you the monthly deposit you need.