Suppose someone offered to sell you a note calling for the payment of $1,000 in

Question

Suppose someone offered to sell you a note calling for the payment of $1,000 in 15 months. They offer to sell it to you for $850. You have $850 in a bank time deposit that pays a 6.76649% nominal rate with daily compounding, which is a 7% effective annual interest rate, 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 EFF% on the note with that of the bank account.

Explanation / Answer

FV = $850(1.07)1.25 = $925.01

amount in bank after 15 months versus $1,000 if you buy the note.

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PV = $1,000/(1.07)^-1.25 = $918.90.

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FVN = PV(1 + I)^N,           

$1,000 = $850(1 + i)^1.25 = $1,000.

$1,000 = $850(1 + i)^456

daily i = 0.00035646,

EAR = EFF% = (1.00035646)^365 - 1 = 13.89%.

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