Question

You buy a new truck for your trailer that costs $65,000. What are your monthly payments for a 5 year loan assuming an annual interest rate of 4.75%? Your down payment was $5,000. Make sure your answer is shown to the nearest whole cent.

Answer 1

Value of the truck = $65000

Downpayment = $5000

=> Loan Amount P = $65000 - $5000 = $60000

Interest Rate = 4.75% or 0.0475/12 monthly

Number of payment periods = n = 5*12 = 60 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]

= 60000*( 0.0475/12)*(1+ 0.0475/12)⁶⁰/((1+ 0.0475/12)⁶⁰-1) = $1125.41