Future Value Annuity Example

Prepared by Pamela Peterson

Problem

Suppose you want to deposit an equal amount each year, starting in one year, in an account that earns 5% interest, compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account each year (for a total of six deposits)?

Solution

The following information is given:

We want to solve for the cash flow.

Using notation, such that:

CF = periodic cash flow
FV = future value
r = interest rate
T = number of cash flows

FV = CF ( ((1 + r)T) - 1 ) / r)

Inserting the known information,

$5,000 = CF (6.8019)

CF = $5,000 / 6.8019 = $735

We can use the future value annuity table to solve for the present value.

FV = CF (factor for r and T)

CF = FV / (factor for r and T)

The discount factor, from the table, is 6.8019. Therefore,

CF = $5,000 / 6.8019

CF = $735