Question

You and your spouse want to buy a house. You feel that you can make monthly payments of $2,100. The bank is offering a loan rate of 4.65% for monthly payments over 30 years. Estimate what you can afford to spend on a home. [Present the answer rounded to no decimal places. For instance 259462]

Answer 1

Let the amount that can be spent on house = P

Interest Rate = 4.65% or 0.0465/12 monthly

Number of payment periods = n = 30*12 = 360 months

Monthly payments = X = $2100

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> P = X[1- (1+r)^-N]/r

=> P = 2100[1- (1+0.0465/12)^-360]/(0.0465/12) = $407,263.40 = $407,263