The compound interest formula for a monthly investment, worked once, with the range of results across returns and horizons.
Invested at an illustrative 7 per cent a year, compounded monthly, 500 a month for 30 years grows to about 609,985. Only 180,000 of that is money paid in; the other 429,985, or 70.5 per cent of the pot, is compound growth. At 4 per cent the same habit ends near 347,025 and at 10 per cent near 1,130,244, so the assumed return matters as much as the saving.
Worked in full in Stock Market Investing for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
This is the calculation behind every "how much will I have" question about a regular investment into a low-cost index fund. It takes one formula, and seeing it worked once makes it easy to check any projection someone shows you.
| Input | Value |
|---|---|
| Monthly investment | 500 |
| Years | 30 |
| Number of monthly payments | 360 |
| Annual return, nominal | 7% |
| Monthly rate (7% ÷ 12) | 0.5833% |
| Payment timing | end of each month |
Each payment compounds for a different length of time: the first for 359 months, the last for none. Adding them all up gives the future value of an annuity.
FV = P × ((1 + i)n − 1) ÷ i
P = 500, i = 0.07 ÷ 12 = 0.005833, n = 360.
(1.005833)360 = 8.1165, so FV = 500 × (8.1165 − 1) ÷ 0.005833 = 609,985.
In Excel: =FV(0.07/12, 360, -500). Add a final argument of 1, =FV(0.07/12, 360, -500, 0, 1), if you invest at the start of each month: that gives 613,544, 3,558 more.
| Years | Paid in | Value |
|---|---|---|
| 10 | 60,000 | 86,542 |
| 20 | 120,000 | 260,463 |
| 30 | 180,000 | 609,985 |
| 40 | 240,000 | 1,312,407 |
After ten years the account holds 86,542 on 60,000 paid in, and looks like a savings account. Between year 20 and year 30 it grows by 349,522, which is 57.3 per cent of the final total, arriving in the last third of the period. The pot is 3.39 times what went in, and most of that multiple is earned late. That is why stopping or pausing in the middle costs far more than it seems to at the time.
The same arithmetic prices delay. Start five years later and contribute for 25 years instead of 30, and the pot at 7 per cent is 405,036: waiting costs 204,950, against only 30,000 of contributions skipped.
The return is the one input nobody controls, so the useful output is a range rather than a single figure.
| Annual return | 10 years | 20 years | 30 years | 40 years |
|---|---|---|---|---|
| 4% | 73,625 | 183,387 | 347,025 | 590,981 |
| 5% | 77,641 | 205,517 | 416,129 | 763,010 |
| 6% | 81,940 | 231,020 | 502,258 | 995,745 |
| 7% | 86,542 | 260,463 | 609,985 | 1,312,407 |
| 8% | 91,473 | 294,510 | 745,180 | 1,745,504 |
| 10% | 102,422 | 379,684 | 1,130,244 | 3,162,040 |
Over ten years the spread between 4 and 10 per cent is modest, 73,625 against 102,422. Over thirty it is more than three to one. Compounding magnifies the assumption along with the money, which is the strongest argument for keeping the one cost you can control, the fee, as low as possible: one percentage point of annual charges works like moving up a row in this table. What one percentage point of fees actually costs puts a figure on it over forty years.
Inflation. 609,985 in thirty years is not 609,985 of today's spending power. At 2.5 per cent inflation it buys what about 290,806 buys today. The real return is (1.07 ÷ 1.025) − 1 = 4.39 per cent, which is why the 4 per cent row is closer to a real-terms picture than the 7 per cent row.
The target, solved backwards. If the goal is 500,000 in thirty years at 7 per cent, the monthly amount needed is 409.85. In Excel: =PMT(0.07/12, 360, 0, -500000). Working back from a goal is often more useful than working forward from a habit.
Annual compounding on annual sums. Treating the saving as 6,000 paid at the end of each year and compounding once a year gives 566,765, which understates the monthly result by 43,221. The money goes in monthly, so it starts compounding monthly.
Simple interest. Applying 7 per cent to each payment only for the years it is invested, without interest on interest, gives 368,475. The difference from 609,985 is the whole point of compounding, and calculators that quote "average return times money invested" are making this error.
The rule of 72 as a forecast. 72 divided by 7 says money doubles in about 10.3 years; the exact figure is 10.24. It is a sound mental check, but it applies to a single lump sum, not to a monthly habit, where every payment has a different doubling clock.
Three things move the result, in order: the number of years, the return, and the monthly amount. Fees reduce the return directly, and a low-cost index fund is the simplest way to keep that leak small. Run your own numbers with =FV(rate/12, years*12, -amount) and look at two or three return assumptions, never one.
The free workbook for this book does this with the early and the late starter side by side, in today’s money as well as in cash. All figures are illustrative and none is a forecast; investing carries the risk of loss.
Use the future value of an annuity: payment times ((1 + i) to the power n, minus 1), divided by i, with i the monthly rate and n the number of payments. For 500 a month at 7 per cent for 30 years, i is 0.5833 per cent and n is 360, which gives 609,985. In Excel, =FV(0.07/12, 360, -500).
At an illustrative 7 per cent a year compounded monthly, 409.85 a month, from =PMT(0.07/12, 360, 0, -500000). At a lower assumed return the amount rises sharply, which is why it is worth solving the target at two or three rates. Remember that 500,000 then will buy about what 238,000 buys today at 2.5 per cent inflation.
On 500 a month at an illustrative 7 per cent, investing for 25 years instead of 30 ends at 405,036 instead of 609,985. The five skipped years hold only 30,000 of contributions, yet they cost 204,950 of final value, because the missing years are the ones that would have compounded longest.
This article is one calculation from Stock Market Investing for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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