Question

3. Suppose you are considering a purchase of a new car. You have figured out that your budget allows for a monthly payment of 375 for the next three and a half years. And you think that you should be able to get a loan at 5.2% APR. Assuming that you will not have any additional money for the purchase beyond the borrowed amount and that taxes and fees associated with the purchase add up to around $680, what is the maximum price you can consider? If at the time of obtaining a loan you are able to get a better APR, say 4.2%, does that substantially alter the prices of cars you can consider?

4. Consider two 10-year bonds: one carries 5% coupon rate, the other is a pure discount bond. Both have have the same standard face value of $1,000. Explain which bond has greater interest rate risk. Illustrate your explanation with a numerical example.

Answer 1

3.

Monthly payment (EMI) = $375

Monthly interest rate (R) = 5.2%/12 = .4333%

Time (n) = 42 months (3.5 years)

So,

Present value of the loan = 375*(1-1/(1+R)^n)/R = 375*(1-1/1.004333^42)/.004333

Present value of the loan = $14371.61

Payment towards tax and other fees = $680

So, maximum purchase amount to be considered = 14371.61-680 = $13691.61

If the APR is 4.2%

Then, monthly interest rate = 4.2%/12 = .35%

Present value of the loan =375*(1-1/1.0035^42)/.0035

Present value of the loan = $14623.33

So, new purchase amount to be considered = 14623.33-680 = $13943.33

So, the lower APR helps the person considered higher purchase amount that is $13943.33 when the annual APR comes down to 4.2%.

So, it alters the price to be considered for purchase.