Question

I want you to calculate what a monthly P&I payment would be if you go with a 15-year mortgage. Use an interest rate of 5.125% on borrowing $165,000. Also, calculate the total amount of interest that you would have paid over the life of the loan (15-years.)  

Please make sure that you provide me with your TI BA Analyst II solution steps (key strokes).

Answer 1

A 15-year mortgage at a rate of 5.125% annual rate; the monthly payment

M = P * (1+r) ^n * r / [(1+r) ^n - 1]

Where M = monthly payment

P = mortgage amount or principal = $165,000

And r = monthly interest rate = annual interest rate/12 = 5.125%/12 = 0.43% or 0.0043

And n = number of months = 15 years *12 = 180 month

Therefore

M = $165,000 * (1+0.0043) ^180 *0.0043 / [(1+0.0043) ^180 – 1] = $1,315.58

A monthly P&I payment is $1,315.58.

The total amount of interest paid = total payment – principal payment

= monthly payment * number of months - principal payment

= $1,315.58 *180 - $165,000

= $236,804.16 - $165,000

= $71,804.16

Therefore total amount of interest paid over the life of the loan (15-years.) is $71,804.16