Question

A truck costing $112,000 is paid off in monthly installments over four years with 7.5​% APR. After three years the owner wishes to sell the truck. What is the amount he needs to pay on his loan before he can sell the​ truck?

Answer 1

Given about a truck loan,

Loan amount PV = $112000

loan period t = 4 years

interest rate r = 7.5% per year compounded monthly

So, monthly loan payment is calculated using PV formula of annuity,

monthly payment PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 112000*(0.075/12)/(1 - (1+0.075/12)^(-12*4)) = $2708.04

After 3 years, remaining balance on the loan is PV of the annuity for the remaining year

So, Value of loan remaining after 3 years = PMT*(1 - (1+r/n)^(-n*t))/(r/n), where t = 1

=> value of loan remaining = 2708.04*(1 - (1+0.075/12)^(-12*1))/(0.075/12) = $31213.90

So, amount he needs to pay on his loan is $31213.90