Question

An automobile dealer has recently advertised for its new car. There are three alternatives of purchasing the car which are explained below.

Alternative 1 The customer can take delivery of a car after making a down payment of Rs. 25,000. The remaining money should be paid in 36 equal monthly installments of Rs. 10,000 each. 86 Engineering Economics

Alternative 2 The customer can take delivery of the car after making a down payment of Rs. 1,00,000. The remaining money should be paid in 36 equal monthly installments of Rs. 7,000 each.

Alternative 3 The customer can take delivery of the car by making full payment of Rs. 3,00,000.

Suggest the best alternative of buying the cars for the customers by assuming an interest rate of 20% compounded annually. Use the annual equivalent method.

Answer 1

Given Data:

Particulars	Alternative 01 (in Rs)	Alternative 02 (in Rs)	Alternative 03 (in Rs)
Down Payment	25000	100000	-
EMI	10000	7000	-
Full payment	-	-	300000
Tenure of EMI	36 months	36 months	36 months
Interest rate	20% per year = 20/12 = 1.67% per month

To find:

Net annual worth per month for all the alternatives

Solution:

Alternative 01

Net annual worth = 25000(A/P,1.67,36) + 10000

(A/P,1.67,36) = [i(1+i)^n / (1+i)^n – 1] = [0.0167(1+0.0167)^36 / (1+0.0167)^36 – 1] = 0.0372

Net annual worth = 25000(0.0372) + 10000

Net annual worth = Rs 10930 per month

Alternative 02

Net annual worth = 100000(A/P,1.67,36) + 7000

(A/P,1.67,36) = [i(1+i)^n / (1+i)^n – 1] = [0.0167(1+0.0167)^36 / (1+0.0167)^36 – 1] = 0.0372

Net annual worth = 100000(0.0372) + 7000

Net annual worth = Rs 10720

Alternative 03

Net annual worth = 300000(A/P,1.67,36)

(A/P,1.67,36) = [i(1+i)^n / (1+i)^n – 1] = [0.0167(1+0.0167)^36 / (1+0.0167)^36 – 1] = 0.0372

Net annual worth = 300000(0.0372)

Net annual worth = Rs 11160

Based on the calculations above Alternative 02 may be preferred among all the alternatives