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3
3. Mr. Smith has arranged for a mortgage loan of $200,000. The annual rate on the loan is 12%. The bank requires Mr. Smith to make payments of $4,212.90 at the end of every month. How many payments will Mr. Smith have to make?
4. You have decided to buy a car, the price of the car is $18,000. The car dealer presents you with two choices:
(A) Purchase the car for cash and receive $2000 instant cash rebate - your out of pocket expense is $16,000 today.
(B) Purchase the car for $18,000 with zero percent interest 36-month loan with monthly payments.
Market interest rate is 4%. Which option above is cheaper? How much do you save?
Expert Solution
3) Computation of Number of Payments using NPER Function in Excel:
=nper(rate,pmt,-pv,fv)
Here,
NPER = Number of Payments = ?
Rate = 12%/12 = 1% compounded monthly
PMT = $4,212.90 each month
PV = $200,000
FV = 0
Substituting the values in formula:
=nper(1%,4212.90,-200000,0)
NPER or Number of Payments = 64.71 or 65 payments
4.
A) Under option A, total cash outflow at the outset is $16,000.
B) Computation of Present Value using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Present Value = ?
Rate = 4%/12 = 0.33333%
Nper = 36
PMT = $18,000/36 = $500
FV = 0
Substituting the values in formula:
=-pv(0.33333%,36,500,0)
PV or Present Value = $16,935.39
Since the PV of option A is lower, that option is cheaper.
Money saved by choosing option A= 16,935.39-16,000 = $935.39
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