Danny bought a camera from Future Shop for $385 at 3% p.a. rate and 4 equal quarterly payments. Determine the size of the quarterly payments if the agreed focal date is the date of the loan.
A) $98.05
B) $96.25
C) $99.14
D) $93.45
E) $128.33

Question

Quizplus · Accepted Answer

The size of the quarterly payments can be determined using the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PV is the present value (amount of the loan), PMT is the payment per period, r is the interest rate per period, and n is the total number of payments. Here, the interest rate per quarter is $3\% \div 4 = 0.75\%$, or 0.0075 in decimal form, and there are 4 payments. Rearranging the formula to solve for PMT gives us: $PMT = PV \times \frac{r}{1 - (1 + r)^{-n}}$. Substituting the given values: $PMT = 385 \times \frac{0.0075}{1 - (1 + 0.0075)^{-4}}$, which calculates to approximately $98.05.

Danny Bought a Camera from Future Shop for $385 at 3