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 ​$16,000. The purchase will be financed with an interest rate of 9.5​% 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)?

​$______ (Round to the nearest​ cent.)

Answer 1

Answer : calculation of Payments to be made in each case :

In case of Semiannual Payment :

Uisng PMT function of Excel

=PMT(rate,nper,pv,fv)

where,

rate is rate of interest per period i.e 9.5% / 2 (As there are two payments in a year therefore divided by 2)

nper is the number of payments i.e 6 * 2 = 12 (As there are two payments in a year therefore multiplied by 2)

pv is the amount Required i.e -16000

fv is future value i.e 0

=PMT(9.5%/2,12,-16000,0)

Therefore Semi annual Payment is 1779.84

In case of Monthly Payment :

Uisng PMT function of Excel

=PMT(rate,nper,pv,fv)

where,

rate is rate of interest per period i.e 9.5% / 12 (As there are 12 payments in a year therefore divided by 12)

nper is the number of payments i.e 6 * 12 = 72 (As there are 12 payments in a year therefore multiplied by 12)

pv is the amount Required i.e -16000

fv is future value i.e 0

=PMT(9.5%/12,72,-16000,0)

Therefore Monthly Payment is 292.40

To compare the annual cash flow in both alternative we can see that

Annual Cash Flow in Semiannual Payment = 1779.84 * 2 =3559.69

Annual Cash Flow in Monthly Payment = 292.40 * 12 =3508.74

By making Monthly payment the principal is also paying month by month , therefore total payment in Monthly option is less than semiannual option.