Question

1. Suppose someone offered to sell you a note calling for the payment of $1,000 15 months from today (456 days). They offer to sell it to you for $850. You have $850 in a bank time deposit which pays a 7 percent nominal rate with daily (365 days per year) 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: (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 account, and (3) by comparing the EAR on the note versus that of the bank account.

Answer 1

Given bank deposit = $850

Bank interest rate =7% annually daily compounding

15 months implies = 456 days

Bond value = $1000

Option (1): by comparing your future value if you buy the note versus leaving your money in the bank

FV = 850 * (1.00018538)^456 = $911.62

Whereas bond value $1000 which is greater than $911.62

So, when comparing in this option it is good to buy note

Option (2): by comparing the PV of the note with your current bank account

PV = 1000/ (1.00018538)^456 = $918.95

Present value of note = $918.95 which is greater than $850 cost.

So, when comparing in this option it is good to buy note

Option (3): by comparing the EAR on the note versus that of the bank account

Let us equate the note value with bank cost

1000 = 850 * (1+ i)^456

On solving this we get i = 0.00035646

This i is daily interest rate

Converting i to EAR i.e., effective annual rate

( 1+ 0.00035646)^365 – 1 = 13.89%

This return 13.89% is greater than 7% rate given by bank.

So, when comparing in this option it is good to buy note.