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)?

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.

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