The Future Value of Regular Savings

Finds what a regular monthly deposit grows to when it compounds. The contributions and the investment gain are shown separately, so you can see how much the compounding earned.

Explanation

This is what a fixed monthly deposit grows to when the returns compound.

FV = P \times \dfrac{(1 + i)^n - 1}{i}

Here $P$ is the monthly deposit, $i$ the monthly rate (annual ÷ 12) and $n$ the number of deposits (years × 12).

Example

Save 30,000 a month for 20 years at 3% a year.

Total contributed — $30000 \times 240 = 7{,}200{,}000$
Future value — 9,849,000
Investment gain — 2,649,000

You put in 7.2 million and ended with nearly 9.9 million.

Compounding pays late

Compare the same plan run for only ten years.

10 years — contributed 3,600,000, ending value 4,192,000, gain of 592,000
20 years — contributed 7,200,000, ending value 9,849,000, gain of 2,649,000

Double the time and the contributions naturally double. But the gain multiplies by four and a half.

Money paid in during the first year works for twenty years; money paid in during the last year works for one month. A pound saved early is worth far more than a pound saved late. That asymmetry is the whole reason time is called the investor's greatest asset.

Watch out

The rate is an expectation, not a promise.

The formula assumes a tidy 3% every single year. Real markets do no such thing. An average of 3% that includes a year down 20% can end very differently depending on when you withdraw.

Taxes and fees are not included either, and tax-sheltered accounts change the take-home figure considerably.