Question

It’s time to buy a new car! This one is very straight forward. Go to your favorite car company’s website and find the total price of a car of your choosing. Calculate the total price of the car after a $200 documentation fee and 6% sales tax. Once you have the total, calculate your monthly car payment and the total amount you would pay back for both loan options below. Decide which of these two loans you would choose. Support your decision with an explanation.

Loan 1 – 60-month loan at 4.9% financing

Loan 2 – 48-month loan at 0.9% financing

Answer 1

Let us better assume that the value of the car is $5,00,000

Now the price of the car after documentation fee and sales tax is as follows.

Price of the car = 5,00,000 + 200 + 5,00,000 * 0.06 = 530200

Hence the required loan amount is 530200

Now we will calculate the monthly installment under the two options

Option-1)

60 month loan with 4.9% financing

Given amount of interest yearly = 4.9%

hence monthly will be 4.9/12 = 0.408333%

The formula for calculating the monthly equalised installments is.

[P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month

Given R = 0.4083333 and N = 60months

Now monthly installment = (530200 * 0.004083 * (1.004083)⁶⁰)/((1.004083)⁶⁰-1)

= 9981.255.

Here IRR or the monthly interest rate will be 0.408333%

Let us make the amortization schedule as follows.

Total Repayment - 9981.26 * 60 = 598875.33

That means total interest we are bearing is 598875.33-530200 = 68675.33

Option -2 )

48 month loan with 0.9% financing.

Given the annual interest is 0.9% hence the monthly interest is 0.9/12 = 0.075%

By using the formula for monthly installments we can calculate the amount of loan installment as follows,

(530200 * 0.00075 * (1.00075)⁴⁸)/((1.00075)⁴⁸-1)

= 530200 * 0.00075 *28.29119

= 11250

Hence the total payment is 11250*48 = 540,000

The amount of interest is 540000 -530200 = 9800

Here IRR is also 0.075%

It is to be noted that under option -2 cost of loan will be less and IRR will also be less but the EMI amount is more. Hence it is better to take the option 2 however it is important to note that the monthly installment is also more in the option -2. Hence correctly speaking for taking option -2 also it depends on the earning capacity of the customer.