Respuesta :
Ari's EMI if including tax, title and license fees in the cost of the car is $684.22.
Ari's EMI excluding tax, title and license fees from the cost of the car is $664.29.
Since there is no mention of whether Ari is paying the tax, title and license fees separately we can either assume that they are part of the total cost to buy the car; or we can assume that Ari will meet these expenses separately. We have the following data:
With Fees Without Fees
Price of the car $25,000 $25,000
Tax Title and License fees $675 $675
Total cost of the car $25,675 $25,000
less: Down payment $2,500 $2,500
Total Loan Amount $23,175 $22,500
Annual Interest rate 4% 4%
Loan period in years 3 3
Interest rate per month (r) 0.33333 % (4%/12) 0.33333 % (4%/12)
Loan period in months (n) 36 (3×12) 36 (3×12)
Since the EMI is a constant payment in dollar terms, we can use the PV of an annuity formula to find the EMI. The Formula is:
[tex] Present Value of Annuity = P * [\frac{1- (1+r)^{-n}}{r} ] [/tex]
where,
r = interest rate per period
n = number of periods.
Substituting the values of r and n in the above equation, we get,
With Fees:
[tex] 23,175 = P * [\frac{1- (1+0.003333333)^{-36}}{0.003333333} ] [/tex]
[tex] 23,175 = P * 33.87076642 [/tex]
[tex] P = $684.2183525 [/tex]
Without fees:
The equation above boils down to:
[tex] 22,500 = P * 33.87076642 [/tex]
[tex] P = 664.2896627 [/tex]
