Question

I'm having trouble knowing where to begin on this economics question.

Car purchase cost: $30,000
Fuel and Maintenance Cost at End of Year 1: $4,000
Incremental increase in Fuel and Maintenance Cost after Year 1: $250/year

(a). (1 pt.) Suppose that you can get a car loan at 7.9% annual, compounded monthly, for a term of 60 months. You put down $3,000 and you finance the remaining $27,000. What is the monthly payment ($/month)?

(b). (1 pt.) What is the present worth of the fuel and maintenance costs ($) if we assume an effective annual interest rate of 7.1 percent, compounded annually? Base your calculation on a lifetime of 10 years.

Please show the formulas you use! Don't just use excel! Thank you!

Answer 1

a) EMI = [P x R x (1+R)ⁿ] / [(1+R)ⁿ-1]

R = (7.9 /100) / 12 = 0.079/12

P= 27000

n = 60 months

EMI = [ 27000*(0.079/12)*( 1 + 0.079/12)⁶⁰ ] / [ (1 + 0.079/12)⁶⁰ -1 ] = 263.508 / 0.4825 = 546.13

EMI = 546.13

b) P = A₁ (P/A,i%,n) + G (P/G,i%,n)

A₁  = 4000

G = 250

i=7.1% =0.071

N = 10

P = 4000*(P/A,7.1%,10) + 250* (P/G,7.1%,10)

(P/A, i, N) =

(P/A,7.1%,10) = 6.99

(P/G, i, N) =

(P/G,7.1%,10) = 27.535

Using these value,

Present worth, P = 4000*6.99 + 250*27.535 = 27960+ 6883.75 = 34,843.75