Question

12. Suppose someone offered to sell you a note that calls for a $1,150 payment four years from today. The person offers to sell the note for $850. You have $850 in a bank time deposit (savings instrument) that pays a 7.0% APR with daily compounding, 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 two ways: (a) by comparing your future value (FV) if you buy the note versus leaving your money in the bank (FV of the note is $1150. compare this to the FV of leaving $850 in the bank for 4 years with daily interest compounding, should you buy the note?) (1 point) (b) by comparing the present value (PV) of the note with your current bank investment (by taking the PV of the note and using your bank's interest rate, you are determining how much money you would need to deposit in the bank today in order to earn that same $1150. Is it more than $850 or less? Remember that we always want to pay (or invest) the minimum today in order to receive a certain amount in the future). (1 point) (c) Based on parts (a) and (b), do you buy the note or keep your money in the bank? Be sure to explain your answer. (1 point)

Answer 1

Solution:

From the question, we have the following information:

Present Value (PV) of bank deposit = $850

Future Value (FV) of note = $1,150

Bank deposit interest rate (r) = 7% APR compounded daily or 0.0192% daily

Total time horizon of investment (n) = 4 years or 1,460 days (considering 365 days in a year)

Solution to Part (a):

Comparing FV of note with FV of leaving money in the bank:

We know that FV of note is $1,150. We can calculate FV of bank deposit using the following formula:

FV = PV * (1+r)n

Using the information provided in the question, we get:

FV = 850*(1+0.0192%)1460 or FV = 850*(1+0.0192/100)1460

FV = 850*1.3235

Hence, FV of bank deposit = $1,125

Considering that FV of note is higher than FV of bank deposit by $25 (1,150-1,125), we should buy the note as it will provide higher value in future.

Solution to Part (b):

Comparing PV of note with PV of leaving money in the bank:

We know that PV of deposit is $850. We can calculate PV of note using the following formula:

PV = FV / (1+r)n

Using the information provided in the question, we get:

PV = 1,150 / (1+0.0192%)1460 or PV = 1,150 / (1+0.0192/100)1460

PV = 1,150 / 1.3235

Hence, PV of note = $869

So, to get $1,150 in future at current bank rate, we should have a deposit of $869. However, by buying the note today for $850, we will get a future value of $1,150.

As we want to invest minimum today, we should buy note (for $850) instead of having bank deposit of $869.

Solution to part (c):

Basis part (a), we clearly see that future value of bank deposit is only $1,125 whereas future value of note is higher at $1,150. To maximise our future benefit, we should buy the note and gain higher future value of $1,150.

Basis part (b), it also clear that to have a future value of $1,150, bank deposit required is $869 whereas buying note, with present value of $850, can also provide as future value of $1,150. Hence, to minimise our investment today, we should buy the note.