Question

An individual agrees to pay $6,000 per year for three years to pay off a car loan. His payments are always made at the end of each year. If the interest rate in year 1 is 3%, in year 2 is 3.5% and in year 3 is 4%, and if compounding is done twice a year, how much did the car originally cost? (That is, work out the price he must have agreed to pay for the car.)

Answer 1

Effective interest rate in year 1 = (1 + 0.03 / 2)^2 -1 = 1.030225 - 1 = 0.030225

Effective interest rate in year 2 = (1 + 0.035 / 2)^2 -1 = 1.03530625 - 1 = 0.03530625

Effective interest rate in year 3 = (1 + 0.04 / 2)^2 -1 = 1.0404 - 1 = 0.0404

original cost of car = 6000 / (1+0.030225) + 6000 / [(1+0.030225) *(1+0.03530625)] + 6000 / [(1+0.030225) *(1+0.03530625) *(1+0.0404)]

= 6000 / (1.030225) + 6000 / [(1.030225) *(1.03530625)] + 6000 / [(1.030225) *(1.03530625) *(1.0404)]

= 16856.25