Question

You wish to purchase a new pickup truck. The dealership offers to finance $40,000 at a 2% annual rate (AR) with 36 monthly payments. The first payment starts 6 months from now. Market interest rates are 4% AR. Determine your true cost of purchasing the pickup (i.e., the present value of your payments).

Please show work. Thank you :)

Answer 1

• As first payment starts after 6 months from now, we shall find future value of the loan amount as follow:-=PV (1+r)ⁿ

= $40000 (1.02) = $40,800

Here, r = 4% AR is given.Hence for 6 months, we shall consider r = 4% *6/12 = 2% = 0.02

• Now, we should calculate the monthly installments to be paid @ 2% AR for 36 months :-

Calculation of the EMI amount is described in the image attached here using annuity formula :

(Note - for this calculation, we should consider $40,800 as the principal loan amount as the repayment will start after 6 months from now.)

• This calculation of monthly EMI can also be done using PMT formula in Excel as follow:-
• PMT(rate, nper, pv, [fv], [type])
• Here, rate = 2%/12

nper = number of periods = 36

pv = present value of principal = $40,800

Calculation of true value i.e. Present value of the loan payments :-

For calculating present value of the loan payments, we shall discount the EMI payments with the Discounting rate of 4% AR.

We shall use PV function in the excel to calculate the present value as follow :-

=PV(RATE,NPER,PMT)

Where,

Rate = 4% / 12	=0.003333
NPer = Number of periods	=36
PMT = Amount of payment	= $1168.62

Hence, we get the True cost of truck = $39,582.06