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Future Value of an Annuity (Regular Deposits)

Also known as regular savings growth · monthly contribution growth · FV of deposits

FV=D (1+i)n−1i\mathit{FV} = D\,\frac{(1+i)^n - 1}{i}
$
$

Worked example: 3 deposits of $1,000 at 5% → $3,152.50 — press Try an example to run it live, then adjust anything.

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See also
Sinking Fund Factor (A/F) — The same relation as the bare multiplier (A/F, i, n) that engineering-economy tables list, for when the question is the factor rather than the money.
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Annuities and loans →

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Future Value of an Annuity (Regular Deposits) explained

FVDin

Put the same amount away at the end of every period and each deposit compounds for a different length of time. The first sits longest, the last earns nothing at all, and adding up that staircase gives FV=D[(1+i)n−1]/i\mathit{FV} = D[(1+i)^n - 1]/i. Three annual deposits of $1,000 at 5% grow to 1000(1.1025)+1000(1.05)+1000=3152.501000(1.1025) + 1000(1.05) + 1000 = 3152.50, which the closed form reproduces exactly.

Read backwards, the same relation is the sinking fund: the deposit you need now to have a known sum later. A contractor who knows a $60,000 truck needs replacing in seven years can ask what monthly transfer gets there, rather than discovering the answer when the old one dies. This is how equipment reserves, roof funds and condominium capital plans are actually built.

The version here assumes deposits at the end of each period, the ordinary annuity. If you deposit at the beginning instead, every dollar earns one extra period, and the whole answer is simply larger by a factor of (1+i)(1+i).

Future Value of an Annuity (Regular Deposits) formula

FV=D (1+i)n−1i\mathit{FV} = D\,\frac{(1+i)^n - 1}{i}
Where
  • FV\mathit{FV}= Future value ($)
  • DD= Deposit each period ($)
  • ii= Interest rate per period
  • nn= Number of deposits

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Part of this formula set

Equipment, depreciation and payback

4 formulasStraight-line and declining-balance depreciation plus simple payback — how a purchase looks on paper and in cash.