Question

n.   Suppose someone offered to sell you a note that calls for a $1,000 payment 15 months from today. The person offers to sell the note for $850. You have $850 in a bank time deposit (savings instrument) that pays a 6.76649%simple rate with daily compounding, which is a 7%effective annual interest rate; and you plan to leave this money in the bank unless you buy the note. The note is not risky—that is, you are sure it will be paid on schedule. Should you buy the note? Check the decision in three ways: (1) by comparing your future value if you buy the note versus leaving your money in the bank, (2) by comparing the PV of the note with your current bank investment, and (3) by comparing the r_EAR on the note with that of the bank investment.

o.   Suppose the note discussed in part n, above, costs $850, but calls for five quarterly payments of $190 each, with the first payment due in 3 months rather than $1,000 at the end of 15 months. Would it be a good investment?

Answer 1

1.

a)

Future value of note=1000

Future value of bank savings=850*(1+7%)^(15/12)=925.01

So you should buy the note

b)

Present value of note=750

Present value of bank investment=1000/(1+7%)^(15/12)=918.90

As to get the same amount, I have to save more in case of Bank, choose note

c)

EAR on the note=(1000/850)^(12/15)-1=13.88%

EAR on bank=7%

As EAR of note is higher, choose note

2.

Present value=190/(1+7%/4)+190/(1+7%/4)^2+190/(1+7%/4)^3+190/(1+7%/4)^4+190/(1+7%/4)^5=902.092

As present value of receiving is more than presnet value of payment (850), it is a good investment