Question

Find the monthly payment on a car that you intend to buy. Use the following inputs:

· Price of the car is 180,000 AED.

· The bank will finance only 75% of the car price.

· The interest rate is 3% and the loan term is 5-year.

What is the down payment? What is the monthly payment?

The bank officer told you that they have a special option for Ajman University Students. The offer is as follows:

· The bank will finance 90% of the car price.

· The interest rate is 4% and the loan term is 4-year.

What is the down payment? What is the monthly payment?

Write a short paragraph that compares the two offers. Which one will you take and why

Answer 1

(a) Price of car = AED 180000

Bank will finance 75% of value

=> Downpayment = 25% of car value = 0.25*180000 = AED 45000

Loan Amount = P = Value of Car - Downpayment = 180000 - 45000 = AED 135000

Interest Rate = 3% or 0.03/12 monthly

Number of payment periods = n = 5*12 = 60 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 135000*( 0.03/12)*(1+ 0.03/12)⁶⁰/((1+ 0.03/12)⁶⁰-1) = AED 2425.77

(b) Price of car = AED 180000

Bank will finance 90% of value

=> Downpayment = 10% of car value = 0.10*180000 = AED 18000

Loan Amount = P = Value of Car - Downpayment = 180000 - 18000 = AED 162000

Interest Rate = 4% or 0.04/12 monthly

Number of payment periods = n = 4*12 = 48 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 162000*( 0.04/12)*(1+ 0.04/12)⁴⁸/((1+ 0.04/12)⁴⁸-1) = AED 3657.81

(c)

We need to find the interest paid over the loan tenure

Interest Paid = Monthly Installment * Number of months - Loan Amount

For (a) , Interest Paid = 2425.77*60 - 135000 = AED 10546.20

For (b) , Interest Paid = 3657.81*48 - 162000 = AED 13574.88

The interest paid to bank is lower in first case (25% downpayment, 3% interest , 5 year) and hence we should take this offer as compared to second option