Question

1.You purchase a $255,000 house, pay 20% down and get a loan for $204,000. The loan is a 30-year fixed-rate mortgage where the annual interest rate is 5.85% and there will be 360 monthly payments. What is the monthly payment?

Answer 1

Value of the home = $255000

Downpayment = 20% of 255000 = $51000

=> Loan Amount P = $255000 - $51000 = $204000

Interest Rate = 5.85% or 0.0585/12 monthly

Number of payment periods = n = 360 months

Let monthly payments made be X

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

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

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

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 204000*( 0.0585/12)*(1+ 0.0585/12)³⁶⁰/((1+ 0.0585/12)³⁶⁰-1) = $1203.48