Question

Suppose you are a mortgage lender.  You have determined that the maximum monthly mortgage payment the borrow can afford is $1200 for 30 years.  Given you want to earn a 6.5 percent rate of return per year compounded monthly, what is the most you are willing to lend the borrower? Show work and what did you do

Answer 1

We can use the present value of annuity formula to calculate amount that you willing to lend the borrower.
Present value of annuity = P * {[1 - (1+r)^-n]/r}
Present value of annuity = amount than I can lend = ?
P = Monthly mortgage payment = $1200
r = rate of interest per month = 6.5%/12 = 0.005417
n = number of months mortgage = 30 years * 12 = 360
Present value of annuity = 1200 * {[1 - (1+0.005417)^-360]/0.005417}
Present value of annuity = 1200 * 158.2108
Present value of annuity = 189852.98
The amount that I am willing to lend the borrower is $1,89,852.98