Question

Sam​ Hinds, a local​ dentist, is going to remodel the dental reception area and add two new workstations. He has contacted​ A-Dec, and the new equipment and cabinetry will cost ​$22,000. The purchase will be financed with an interest rate of 8​% loan over 8 years. What will Sam have to pay for this equipment if the loan calls for quarterly payments ​(4 per​ year) and weekly payments ​(52 per​ year)? Compare the annual cash outflows of the two payments. Why does the weekly payment plan have less total cash outflow each​ year?What will Sam have to pay for this equipment if the loan calls for quarterly payments ​(4 per​ year)?

Answer 1

Answer:

Sam will pay $937.43 weekly or $71.64 quarterly.

The weekly plan has less total cash outflow each year because it involves lower interest charges as the payment is made more frequently.

Sam will have to pay $117.18 if the loan calls for quarterly payments.

Explanation:

The cash outflows are calculated using the PMT formula or function as follows.

Quarterly Payment:

PMT(rate = 0.08/4, nper = 8x4, pv = 22000, fv = 0, 0) = $937.43

Weekly Payment:

PMT(rate = 0.08/52, nper = 8x52, pv = 22000, fv = 0, 0) = $71.64

Annual cash outflow using quarterly payment = $937.43 x 4 = $3749.72

Annual cash outflow using weekly payment = $71.64 x 52 = $3725.28

The weekly plan has $3749.72 - $3725.38 = $24.44 less total cash outflow each year because it involves lower interest charges as the payment is made more frequently.

Sam will have to pay $3749.72 / 32 = $117.18 if the loan calls for quarterly payments.