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Finance·1 min read·

Savings with monthly deposits

See a balance after monthly deposits compound at a yearly rate, starting from an amount you already have.

The answer

The amount you already have grows by the monthly rate. Each deposit is added at the end of the month and then grows with the later months. The balance is those two pieces added.

Result

$6,142.13

Balance at the end

Deposited along the way
$4,800.00

How this works

Let r be the annual rate divided by 12 and by 100, and n the number of months. The starting amount becomes start × (1+r)^n. The deposits become deposit × ((1+r)^n − 1) ÷ r. A zero rate is the start plus deposit × n. Deposits land at the end of each month, so the last deposit earns no interest in this formula.

$1,000 already saved, plus $200 a month, at 5% for 2 years, ends at $6,142.13. You deposited $4,800 along the way. A withdrawal, a skipped month, or a rate that changes is a different series than the one this page runs.

Examples

  • $1,000 saved, $200 a month, 5% for 2 years

    The balance is $6,142.13. The deposits add up to $4,800.

Common mistakes

  • ×

    Comparing this with a lump-sum compound result and expecting them to match.

  • ×

    Putting the deposit at the start of the month when this formula adds it at the end.

Frequently asked questions

What if the rate is zero?

The balance is what you have now plus every deposit. No interest is added.

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