Future Value of an Annuity
Accumulated value of regular contributions.
Formula
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Example
P=$5k, r=5%, n=30: FV ≈ $332,200
How it works
This formula finds how much a series of equal payments will grow to if each payment earns interest over time. It works by adding the future value of each deposit: the first payment compounds for the full number of periods, the next for one fewer period, and so on, which creates a geometric series that simplifies to the closed form shown.
When to use it
Use it when you make regular end-of-period deposits into an account, fund, or savings plan and want the total balance at the end. It is common in retirement planning, loan sinking funds, and other actuarial calculations involving level contributions.
Worked example, step by step
Suppose you deposit P = $250 at the end of each month into an account earning r = 0.6% per month for n = 48 months. FV = P((1 + r)^n - 1) / r FV = 250((1.006)^48 - 1) / 0.006 (1.006)^48 ≈ 1.3251 FV ≈ 250(1.3251 - 1) / 0.006 FV ≈ 250(0.3251) / 0.006 FV ≈ 81.275 / 0.006 FV ≈ $13,546 So the annuity will grow to about $13,546.
Common mistakes to avoid
- Using the annual interest rate with monthly payments without converting the rate and number of periods to the same time unit
- Forgetting that this version assumes payments are made at the end of each period, not the beginning
- Dividing by r when r is zero; if there is no interest, the future value is just P × n
Did You Know?
Starting an annuity ten years earlier can nearly double the final pot, thanks to compounding.
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