# Calculating a Monthly Payment

We will look at two methods using the TI-84 calculator to find a monthly payment on a mortgage. There is a complicated formula for calculating the the monthly payment on a mortgage, and an app callled TVM solver that using the mortgage formula that can determine the monthly payment. MATH 1001 at MGA suggests that you use the TVM app method.

METHOD 1: Using the TVM App

Problem: What will be the monthly mortgage payment on a 30 year mortgage when purchasing a home for \$185,000 if there is a 15% down payment, and the mortgage rate is 2.7%.

Solution:

Note that the required formula and explanation of each letter in the formula is found at the bottom of this file.

First we must determine how much money we are mortgaging. The purchase price is \$185,000 but a down payment of 15% of the price will be made, decreasing the amount to be mortgaged by 15% as follows: To find the TVM app, press and then press again. Now you are in the TVM app. The screen that you see are below.   We must fill in a number for the letters used in the TVM letters. The meaning of the letters is as follow:

 N Total number of payments over the life of the mortgage I% Interest rate as a percent -- no % sign PV Present Value or Principal Value; the initial value of the loan PMT Payment amount per period; this is what we are trying to figure out in this problem! FV Future value; we leave this as 0 because we want to pay the loan off P/Y Number of payments per year; We assume 12 for a mortgage (once a month) C/Y Number of compounding periods per year; we will assume monthly (12) in mortgage calculations PMT When payment occurs; Choose END for mortgages

So we identify the number to be used for each letter. This is a 30 year mortgage with 12 monthy payments per year. Thus N = 30x12 = 360. The interest rate is 2.7%, so we use I = 2.7. The amount we are financing after the down payment is PV = 157,250. PMT is what we are trying to find, so we leave that 0 for nowWe use FV = 0 to pay off the loan, the future value will be zero. P/Y = 12, the number of payments per year, and C/Y = 12 as a mortgage is compounded month. For a mortgage we choose PMT = END. If END is not already highlighted, move the cursor to END and press ENTER. The screen now looks like the screen below. Now we calculate the payment. Move the flashing cursor back up to PMT. Next press to solve. The monthly mortgage payment will be displayed next to PMT with a negative sign since this is money going out. Ignore the negative sign.  The monthly mortgage payment on this loan rounded to the nearest cent is \$637.80.

METHOD 2: Using the Mortgage Formula

Problem: What will be the monthly mortgage payment on a 30 year mortgage when purchasing a home for \$185,000 if there is a 15% down payment, and the mortgage rate is 2.7%.

Solution:

Note that the required formula and explanation of each letter in the formula is found at the bottom of this file.

First we must determine how much money we are mortgaging. The purchase price is \$185,000 but a down payment of 15% of the price will be made, decreasing the amount to be mortgaged by 15% as follows: So we know the amount to be financed is P = \$157,250. The mortgage interest rate is 2.7%, so converting to a decimal, we know that r = .027. This is a 30 year mortgage, so t = 30, and there are 12 monthly payments in a year, so n = 12. Thus starting with the formula, and substituting, we have  Now we will use our TI-84 to evalute the above expression. Since the entire expression is a fraction, we start with to get a fraction template. We now start by filling in the numerator by pressing the following keys. The screen results are below the keypresses. Note that we needed another fraction template within the numeration.  Next use the down arrow to get to the denominator of the fraction and enter the denominator of the formula using the following keypresses. The result screen is below.   Now right arrow twice and press ENTER to see the monthly payment.   The monthly mortgage payment on this loan rounded to the nearest cent is \$637.80. The above formula can be used to find any kind of monthly payment and not just mortgages. Frequently loans of smaller amounts do not required a down payment, and the entire amount is financed.