How the balance grows
Compound interest means each period's interest is added to the balance, and the next period earns interest on the larger amount. Monthly deposits join the balance and start earning too. The calculator converts the yearly rate to its monthly equivalent, so it also works when interest compounds quarterly, yearly or daily.
FV = P x (1 + rm)^M + C x [(1 + rm)^M - 1] / rm, where P is the starting amount, C is the monthly deposit, M is the number of months and rm = (1 + r/n)^(n/12) - 1 is the monthly rate for a nominal yearly rate r compounded n times a year. For deposits at the start of each month, multiply the second term by (1 + rm). It is the standard future value of an annuity formula.
A worked example: start now or wait ten years
Someone starts with $2,000 and adds $150 a month for 40 years at 7% a year, compounded monthly. Their deposits total $74,000. The balance at the end is $426,344.83, so $352,344.83 of it is interest. Interest becomes larger than the total contributed in year 18 and keeps pulling away after that.
| Plan | Years saving | Put in | Final balance |
|---|---|---|---|
| Start now | 40 | $74,000 | $426,344.83 |
| Start 10 years later | 30 | $56,000 | $199,228.64 |
| Cost of waiting | 10 | $18,000 | $227,116.19 |
The late starter puts in $18,000 less but ends with $227,116.19 less, because the first ten years of deposits get the most time to compound. At 7%, money roughly doubles every ten years, which is the Rule of 72 at work: 72 / 7 is about 10.3. Change the delay in the calculator to see how the gap grows or shrinks.
What the result leaves out
The calculator uses one fixed rate for the whole period. Real investments move up and down, and a savings account rate changes over time, so treat the output as one scenario and try a lower rate as well. Fees, taxes and inflation all reduce what the money buys. A rough way to account for inflation is to subtract the expected inflation rate from the rate you enter.
Compounding frequency matters less than most people expect. A 7% rate compounded monthly equals 7.23% a year, against 7.00% for annual compounding. Consistent deposits and enough years move the answer far more than the compounding schedule does.
Mistakes to avoid
- Treating the result as a promise. A steady 7% is an assumption, and actual returns arrive unevenly.
- Leaving out fees, taxes and inflation, which can cut the real growth noticeably.
- Entering a yearly deposit in the monthly box.
- Comparing a nominal rate with an effective rate as if they were the same thing.
- Stopping deposits in a downturn. Missing deposits early costs the most because they would have had the longest to grow.
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