Question

Nader plans to buy a used car. He can afford to pay $280 at the end of each month for three years. The best interest rate he can find is 9.8%la, compounded monthly. For this interest rate, the most he could spend on a vehicle is $8702.85. Determine the amount he could spend on the purchase of a car if the interest rate is 9.8%/a, compounded annually.

Answer 1

The amount of most spending (PV) should be here.

Given,

Monthly payments = A = 280

Rate of interest = r = 0.098 per month

Number of months in a year = m = 12

Number of years = m = 3

PV = (A/r/m) × [1 – (1 + r) ^ (- n)]

      = (280 / 0.098/12) × [1 – 1/1.098^3]

      = 34,285.71 × [1 – 1/1.32375]

      = 34,285.71 × [1 – 0.75542]

      = 34,285.71 × 0.244572

      = 8,385.33 (Answer)

Note: the figure under monthly compounding must be higher than yearly compounding, since the number of compounding increases.