## 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:

- periodic cash flow = $5,000
- interest rate = 5%
- number of cash flows = 6

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__