# Maths problem help

1. May 14, 2005

### IB

a 30 year mortgage is obtained on a $275,000 home at a rate of 7.25%. The monthly payment is$1,875.99. After making payments for 8 years, what is the balance due on the mortgage?

2. May 14, 2005

### OlderDan

Let B(n) = balance after n payments
I(n) = monthly interest payment
A = amount of payment = $1,875.99 i = montly interest rate = 7.25%/12 I(n) = B(n-1)i B(0) =$275,000
B(1) = B(0) - (A - I(1)) = B(0) - (A - B(0)i)
B(2) = B(1) - (A - I(2)) = B(1) - (A - B(1)i)
B(3) = B(2) - (A - I(3)) = B(2) - (A - B(2)i)

etc

Problems like this can easily be done on a spreadsheet. You can also start expanding out the terms and see a progression. If you are learning how to do sums of series, then maybe that is what you are supposed to be doing here. The resulting formula involves a ratio involving exponential functions. The notation is a bit different, but you can find the result and other mortgage related equations here

http://www.econ.umn.edu/~cswan/econ5623/MortMath/MortMath.html

3. May 14, 2005

### IB

Can you do it on a TI-calculator?

4. May 15, 2005

### OlderDan

There are financial functions built into the TI-83 Plus, and probably the TI-83, and probably other calculators as well. You could also program many calculators to do this calculation. Get out your manual, or go to the TI website to download a manual. The financial function on the TI=83 Plus are under APPS. There is a data entry area for entering the parameters given in the problem, and a number of functions including one for balance. Be careful when you enter the data that you specify the data consistently. There are some functions that do not need all the data specified, and some that do not work unless you have the right set of data specified.

For example if you give it N=360, I=7.5%, PV=275000, and P/Y = 12, it will correctly calculate the payment as -1875.98477, but if you ask it for the balance after some number of payments and you have not filled in the correct payment, it will give you the wrong answer assuming the payment is whatever you put into (or was left in) the data bank. It works, but you have to be careful. It does not check for inconsistent data.