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Formula

FV = P(1 + i)ⁿ + pmt × ((1 + i)ⁿ − 1) ÷ i, with i the monthly return and n the number of months

The starting amount compounds on its own, and each monthly addition compounds from the month it goes in. The second term is the future value of an ordinary annuity — deposits made at the end of each period — so the last deposit earns nothing and the first earns for almost the whole span.

Worked example

$10,000 to start and $500 a month for 10 years at 6% grows to about $100,134. Of that, $70,000 is money paid in and about $30,134 is growth.

Where this can give the wrong answer

• A steady return is a simplification. Real investments rise and fall, and the order of good and bad years changes the outcome even when the average is the same.
• The result is in future money. At 3% inflation, a sum ten years from now buys about a quarter less than it would today.
• Fees and taxes are not deducted. A 1% annual fee is equivalent to entering a return one point lower, and over decades that difference is large.
• Additions are counted at the end of each month. Investing at the start of the month instead would give a slightly higher figure.

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