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 ​$25 comma 000. The purchase will be financed with an interest rate of 10​% loan over 6 years. What will Sam have to pay for this equipment if the loan calls for semiannual payments ​(2 per​ year) and monthly payments ​(12 per​ year)? Compare the annual cash outflows of the two payments. Why does the monthly payment plan have less total cash outflow each​ year? What will Sam have to pay for this equipment if the loan calls for semiannual payments ​(2 per​ year)?

Answer 1

Answer:

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

• $2,820.62

and monthly payments ​(12 per​ year)?

• $531.13

Compare the annual cash outflows of the two payments.

• total semiannual payments per year = $2,820.62 x 2 = $5,641.24
• total monthly payments per year = $531.13 x 12 = $6,373.56

Why does the monthly payment plan have less total cash outflow each​ year?

• The monthly payment has a higher total cash outflow ($6,373.56 higher than $5,641.24), it is not lower. Since the compounding period is shorter, more interest is charged.

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

• $2,820.62 x 12 payments = $33,847.44 ($25,000 principal and $8,847.44 interests)

Explanation:

cabinet cost $25,000

interest rate 10%

we can use the present value of an annuity formula to determine the monthly payment:

present value = $25,000

PV annuity factor (5%, 12 periods) = 8.86325

payment = PV / annuity factor = $25,000 / 8.8633 = $2,820.62

present value = $25,000

PV annuity factor (0.8333%, 60 periods) = 47.06973

payment = PV / annuity factor = $25,000 / 47.06973 = $531.13