Question

An individual agrees to pay $6,000 per year for three years to payoff 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+3%/2)^2 -1 = 3.00225%

Effective interest rate in year 1 = (1+3.5%/2)^2 -1 =

Present value of the loan payment = 6000/(1+3%/2)^2 + 6000/(1+3.5%/2)^4 +  6000/(1+4%/2)^6

Present value of the loan payment = $16749.55 or $16750

So, price he must be agreed to pay is $16749.55 or $16750.