Question

Suppose someone offered to sell you a note calling for the payment of $1,000 15 months from today. They offer to sell it to you for $850. You have $850 in a bank time deposit which pays a 7% effective annual interest rate (compounding), and you plan to leave the money in the bank unless you buy the note. The note is not risky--you are sure it will be paid on schedule. Should you buy the note?
Check the decision in three ways:

a. By comparing your future value if you buy the note versus leaving your money in the bank.
b. By comparing the PV of the note with your current bank account.
c. By comparing the EFF% on the note with that of the bank account.

Answer 1

Answer:

1. The future value = 1000

Now we are to calculate the future value of bank savings

= 850x(1+0.07)^15/12

= 850x1.07^1.25

=$925.0147

So it is better to buy note.

2. Present value = 1000/(1.07^15/12)

= 1000/1.08825252622

= $918.9

For one to get same amount of money then savings would have to be increased. So we choose note

3. EAR = EFF%

= 1000/(850^12/15)-1

= 13.88%

We have EAR on bank as 7% and that of note as 13.88%. note is higher so we choose note