Question

A car costs $25,000 plus $675 for tax, title, and license fees. ari finances the car by putting down $2,500 in cash and taking out a 3-year, 4% loan. what will his monthly payments be (if figured across all 3 years rather than annually)?

Answer 1

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:

$Present Value of Annuity = P * [\frac{1- (1+r)^{-n}}{r} ]$

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:

$23,175 = P * [\frac{1- (1+0.003333333)^{-36}}{0.003333333} ]$

$23,175 = P * 33.87076642$

$P = 684.2183525$

Without fees:

The equation above boils down to:

$22,500 = P * 33.87076642$

$P = 664.2896627$