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.  The purchase will be financed with an interest rate of 7.5​% 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?

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 7.5% / 4 (As there are two payments in a year therefore divided by 4)

nper is the number of payments i.e 8 * 4 = 32 (As there are two payments in a year therefore multiplied by 4)

pv is the amount Required i.e -20000

fv is future value i.e 0

=PMT(7.5%/4,32,-20000,0)

Therefore Quarterly Payment is 836.81

In case of Weekly Payment :

Uisng PMT function of Excel

=PMT(rate,nper,pv,fv)

where,

rate is rate of interest per period i.e 7.5% / 52 (As there are 52 payments in a year therefore divided by 52)

nper is the number of payments i.e 8 * 52 = 416 (As there are 52 payments in a year therefore multiplied by 52)

pv is the amount Required i.e -20000

fv is future value i.e 0

=PMT(7.5%/52,416,-20000,0)

Therefore Weekly Payment is 63.97

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

Annual Cash Flow in Quarterly Payment = 836.81 * 4 =3347.24

Annual Cash Flow in Weekly Payment = 63.97 * 52 = 3326.30

By making Monthly payment the principal is also paying month by month and interest expense is also less , therefore total payment in Weekly option is less than Quarterly option.