# Knowledge Base

## Solution 11200: Calculating for a Mortgage's Annuity Factor Using the BA-35 Solar or the BA Real Estate™.

### How do I calculate for a mortgage's annuity factor using the BA-35 Solar or the BA Real Estate?

The example below will demonstrate how to calculate for a mortgage's annuity factor using the BA-35 Solar or the BA Real Estate.

Usually, a mortgage calculation is done as follows:

Loan: $100,000 PV Interest: 10% I/Y N= 25 years Note: Requires 25 annual payments *very important Compute for PMT=$11,017 annually.

Since the annual payments are equal, they are considered an annuity. The present value can now be calculated. Using a discount rate, the present value of the annuity is equal to the amount of the loan:

Annual payment x Annuity factor = Present Value of payments

11017 x 9.077 = $100,000 In this case "9.077" is the annuity factor. It can be calculated by solving for the present value of a$1-per-year payment, discounted at 10% for 25 years.

On the BA Real Estate, make sure P/Y is set to 1 for annually. Press [2nd][I%][=].
TERM = 25
I% = 10
PMT = -1
CPT for LOAN = 9.077

On the BA-35 Solar:

N = 25
%i = 10
PMT = 1
CPT for PV = 9.077

In conclusion:

To find an annuity factor, use the number of years, the annual interest rate, $1.00 for payment, then compute for the Present Value, which will determine the annuity factor. By definition, annuity factor is the Present value of$1 paid for each t or n periods.

The annuity factor is usually given on the back of a finance book as "Present Value of an Annuity of \$1 for n Periods".

Please see the BA-35 Solar and BA Real Estate guidebooks for additional information.