Finance Tutor Help ASAP: APR/ IRR Please answer all questions from a through e Y

Question

Finance Tutor Help ASAP: APR/ IRR Please answer all questions from a through e

You’re given with a 5-year auto loan from your credit union. Suppose the total loan you have is $25,000 and the current market interest rate is 5.2% for the short-term loans with the same creditability as yours. Answer the following questions: (Show Solution)

a)Given that the APR (namely the Annual Percentage Rate. That is, the stated interest agreed on the loan) of the loan is 5.2% per year, what is the monthly payment if you’re intended to have the loan for 5 years?

b)What is the effective annual rate if the loan is compounded monthly?

c)Suppose the credit union says that if you’d like to retire the loan earlier, say at the end of the 3rd year, you need to pay (say) $13,000 for the rest of the loan, would you take it given that you have no difficulty to generate the cash flow? Why or why not?

d)Suppose the original agreement that you signed with credit union is to have a 3-year loan and pay back the loan with $13,200 at the end of year 3, how much will be your monthly payment now?

e)Given that the present value of the loan which is $25,000 now, what is the Internal Rate of Return (IRR) for this loan? Is this rate different from the 5.2% market interest rate? Why or why not?

Thank you for the assistance.

Explanation / Answer

The total loan amount = 25000

Interest rate = 5.2 %

Monthly interest = 5.2/ 12 = 0.433%

n= 5 * 12 months = 60

Loan = Annuity * PVIFA ( r%, n)

25000 = A * PVIFA ( 0.433%,60)

A= $474.03

If the loan is compouned monthly, the stated interest is

r = ( 1+ r/12)^12 - 1

12

=(1+ 0.052/12)^12 - 1 = 5.32%

Monthly interest = 5.32/ 12 = 0.4435%

At the end of 3rd year, we will be left with 60 - 36 = 24 installments. The decision to prepay the loan depends on the present value of the loan.

PV = 474 * PVIFA ( 0.433%, 24) = $10782

The early payment required payment of 13000 , which is much higher than the current operating option of paying 474 a month. So the borrower should continue to pay as per the current scheme.

If the terms are changed

25000 = A PVIFA (0.433% ,36) + 13200 PVIF (0.433%, 36)

Solving we get

25000 = A PVIFA ( 0.433 % , 36) + 11298.54

13701.46 = A PVIFA( 0.433%, 36)

A = $411.85

D) For IRR we assume , PV of inflows = PV of outflows

or, 25000 = 474 PVIFA ( r%,60)

or, r = 0.433%

r = 0.433 * 12 = 5.2 %

This rate is same as market rate of return , because we calculated the EMI based on the same rate of interest.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.