## 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:

- future value = $5,000
- interest rate = 5%
- number of cash flows = 6

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__