Present Value Annuity Example

Prepared by Pamela Peterson Drake

Problem

Suppose you determine that you can pay $5,000 per year on a loan. If the loan is for a period of six years and the interest charged is 5% per year, how much can you borrow?

Solution

The following information is given:

We want to solve for the present value.

Using notation, such that:

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

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

Inserting the known information,

PV = $5,000 (5.0757)

PV = $25,378

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

PV = CF (present value annuity factor for r and T)

The factor, from the table, is 5.0757. Therefore,

PV = $5,000 (5.0757)

PV = $25,378