Question

a) To purchase a new vehicle, $3000 is paid as a down payment, followed by bi-weekly payments of $175 for four years. If interest on the loan is 0.20% p.a. compounded bi-weekly, what is the cash value of the vehicle?

b) To purchase a $25 000 vehicle, a loan was taken out with the bank at 3.51% compounded quarterly. Payments will be made at the end of each quarter for the next 3 years. Calculate the size of the payment required to pay off the loan.

c) If $475 000 is saved for retirement, what rate of interest, compounded quarterly, will provide payments of $9726 at the end of every 3 months for the next 15 years?

Answer 1

a). Loan Amount = Bi-weekly payment * [{1 - (1 + r)^-n} / r]

= $175 * [{1 - (1 + 0.002/26)^-(4*26)} / (0.002/26)]

= $175 * [0.0080 / 0.00008]

= $175 * 103.5811 = $18,126.70

Cash Value of Vehicle = Down payment + Loan Amount  

= $3,000 + $18,126.70 = $21,126.70

b). Quarterly Payment = [Loan Amount * r] / [1 - (1 + r)^-n]

= [$25,000 * (0.0351/4)] / [1 - {1 + (0.0351/4)}^-(3*4)]

= $219.375 / 0.0995 = $2,204.06

c). To find the rate, we need to put the following values in the financial calculator:

N = 15*4 = 60;

PV = 0;

PMT = -9726;

FV = 475000;

Press CPT, then I/Y, which gives us 0.72

Periodic Rate = 0.72%

Rate charged = Periodic Rate * No. of periods compounded in a year

= 0.72% * 4 = 2.89%