Zahid purchased a large-screen TV at a local store in December, that had advertised, "No payment for 6 months." Amount to be paid after 6 months is $1495 plus HST (13%) plus an administration fee of $79. If money is worth 2.5%, what is the actual cost of the TV to Zahid on the day of the purchase?
A) $1746.52
B) $1790.45
C) $1476.54
D) $1554.57
E) $1768.35

Question

Quizplus · Accepted Answer

The cost of the TV after 6 months will be:
$1495 + ($1495 * 0.13) + $79 = $1780.35

To find the actual cost to Zahid on the day of purchase, we need to calculate the present value of $1780.35, six months from now. Using the formula for present value of a single sum:
PV = FV / (1 + i)n
where PV is the present value, FV is the future value, i is the interest rate, and n is the number of periods.

PV = $1780.35 / (1 + 0.025)6
PV = $1497.26

This is the actual cost of the TV to Zahid on the day of purchase. Adding the HST and administration fee, the total cost is:
$1497.26 + ($1497.26 * 0.13) + $79 = $1746.52

Therefore, the best choice is A.

Zahid Purchased a Large-Screen TV at a Local Store in December