Question

Determine the costs of buying this car.

a. The sales price of the car is $22,120. State sales tax (CT = 6.35%) must also be paid up front. You will also pay 10% of the car price, and finance 90% of the price.

b. The cost of license and fees is the same whether we buy or lease, so it will not be included.

c. The value of the car in six years is estimated at $6,845.

d. Determine the monthly payment based on a five-year loan at 4.21% annual interest. Assume that you will have a down payment to cover the sales tax.

e. Calculate the equivalent uniform monthly cost of owning the car. This includes up-front fees, monthly payments, and salvage value. Show all assumptions, costs, and calculations.

Answer 1

d.

Sales tax on car = 22,120 * 6.35% = $1,404.62

Down Payment = sales tax = $1,404.62

Loan amount = $22,120

EMI = P * r * (1 + r)ⁿ / ((1 + r)ⁿ - 1)

where P = Principal loan amount = $22,120

r = rate of interest calualted in monthly basis = 4.21% p.a = 4.21 / 1200 = 0.0035

n = number of periods in months = 5 years = 5 * 12 = 60 months

So, EMI = 22,120 * 0.0035 (1 + 0.0035)⁶⁰ / ((1 + 0.0035)⁶⁰ - 1)

= 22,120 * 0.0035 (1.2332258213) / (1.2332258213 - 1)

= 22,120 * 0.0035 (1.2332258213) / 0.2332258213

= 22,120 * 0.0035 * 5.2876899068

= $409.37 Ans.

e.

Equivalent uniform annual cost = P * (A/P,i%,n)

where P = initial asset cost = sale price of the car + sales tax - residual value = 22,120 + 1,404.62 - 6,845 = $16,679.62

i = annual interest rate = 4.21%

n = number of years = 6

So, Equivalent uniform annual cost = 16,679.62 ( A/P,4.21%,6)

= 16,679.62 * 0.1908

= $3,182.47

Equivalent uniform monthly cost = 3,182.47 / 12 = $265.21 Ans.