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 $22,000.

The purchase will be financed with an interest rate of 8% loan over 7 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?

Answer 1

Calculation of semi-annual payment:

PV = $22,000
Rate = 8% / 2 = 4%
Nper = 7 * 2 = 14
FV = 0

Semi-annual payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(4%,14,-22000,0)
= $2,082.72

Semi-annual payment = $2,082.72

Calculation of monthly payment:

PV = $22,000
Rate = 8% / 12
Nper = 7 * 12 = 84
FV = 0

Monthly payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(8%/12,84,-22000,0)
= $342.90

Monthly payment = $342.90

Monthly payment plan have less total cash outflow each​ year. As more payment are made each year, the principal is repaid and thus the interest expense is lower.