Question

island news purchased a piece of property for $1.79 million. The firm paid a down payment of 20 percent in cash and financed the balance. The loan terms require monthly payments for 20 years at an APR of 4.75 percent, compounded monthly. What is the amount of each mortgage payment?

Answer 1

Value of the property = $1790000

Downpayment = 20% of 1790000 = $358000

=> Loan Amount P = $1790000 - $358000 = $1432000

Interest Rate = 4.75% or 0.0475/12 monthly

Number of payment periods = n = 20*12 = 240 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]

= 1432000*( 0.0475/12)*(1+ 0.0475/12)²⁴⁰/((1+ 0.0475/12)²⁴⁰-1) = $9253.92