Question

Present value with periodic rates.

  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

​$20,000.00 The purchase will be financed with an interest rate of 7.57 % loan over 7 years.

A )What will Sam have to pay for this equipment if the loan calls for semiannual payments ​(2 per​ year)

B) What will Sam have to pay for this equipment if the loan calls for weekly payments​(52 per​ year)?

C)Compare the annual cash outflows of the two payments. Why does the weekly payment plan have less total cash outflow each​ year?

Answer 1

A]

semiannual loan payment is calculated using PMT function in Excel :

rate = 7.57% / 2   (converting annual rate into semiannual rate)

nper = 7*2 (7 year loan with 2 semiannual payments each year)

pv = 20000 (loan amount)

PMT is calculated to be $1,866.60

X for A1 - A 1 ($1,866.60)! =PMT(7.57%/2,7*2,20000) D E F B C

B]

weekly loan payment is calculated using PMT function in Excel :

rate = 7.57% / 52   (converting annual rate into weekly rate)

nper = 7*52 (7 year loan with 2 weekly payments each year)

pv = 20000 (loan amount)

PMT is calculated to be $70.82

А2 х v ft =PMT(7.57%/52,7*52,20000) B C D E 2 ($70.82)!

C]

Annual cash outflow of semiannual loan = $1,866.60 * 2 = $3,733.21

Annual cash outflow of weekly loan = $70.82 * 52 = $3,682.72

The weekly payment plan has less total cash outflow each​ year because with the weekly loan, a higher amount of principal is paid off earlier in the loan, which decreases the interest expense, and thereby decreasing the total payments over the loan term.