How to Find the Future Value of an Annuity

The future value of a series of payments is the effective monetary value of those funds when the payments stop. For instance, suppose you are given three equal payments: $1300 in one year, $1300 in two years, and $1300 in three years. If you could invest your money in an account that earns 4% interest per year, then in three years you would have

$1300(1.04²) + $1300(1.04) + $1300
= $4058.08.

Thus, the future value of this annuity is $4058.08. Knowing how to compute FV will help you compare different annuity and lump sum options.

FV of an Annuity

If you are set to receive yearly payments of $P for n years (starting 1 year from now and finishing at the end of Year n ), and the annual interest rate is r (expressed as a decimal), then the future value of those payments is

FV = P(1+r)^n-1 + P(1+r)^n-2 + ... + P(1+r) + P
= P[1+ (1+r) + (1+r)² + ... + (1+r)^n-2 + ... + (1+r)^n-1]
= (P/r)[(1+r)ⁿ - 1]

FV of an Annuity Due

An annuity due is when the payments start immediately. To compute the future value of an annuity due at the end of n years, just multiply the formula above by a factor of (1+r). This factor accounts for the extra year of interest.

FV_Due = (P/r)[(1+r)ⁿ⁺¹ - (1+r)]

Example

You are presented with three options for payment. Option A: $7000 now. Option B: $15000 five years from now. Option C: five equal annual payments of $2500, receiving with the first payment now, and the last payment at the beginning of the fifth year. (Option C is an annuity due.) Assume that you can invest your money in a scheme that earns 6.5% annually.

We can compare these three choices by computing future values at the end of 5 years. We use n = 5 for the number of payments and r = 0.065

FV_A = $7000(1.065)⁵ = $9590.61

FV_B = $15000 (because it is already five years in the future!)

FV_C = ($2500/0.065)[1.065⁶ - 1.065] = $15159.32

Option C has the highest future value under these conditions.

© Had2Know 2010