Question

12. Suppose someone offered to sell you a commercial note (like a corporate bond, this is a short term obligation or loan) that calls for a single $3,750 payment, five years from today. The person offers to sell the note for $3000. You have $3,000 in a bank time deposit (savings account) that pays a 4.75% 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 $3750, compare this to the FV of leaving $3,000 in the bank for 5 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 $3750. Is it more than $3000 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

a. Future value of both the options

Commercial note: Fv after 5 years= 3750

Future value of bank deposit:

interest rate- 4.75% daily compounding

Principal amount= 3000

Term= 5 years

Fv of bank deposit= 3000(1 + Interest Rate / 365 ) ^ (n * 365)= 3000(1.00013)^(5x365) = 3000 + 3000(1.00013^1825) =3000(1.2677)

= 3803.21

hence, bank deposit is more profitable to invest in looking at the future value.

2. Pv of Commercial note when discounted at 4.75% pa daily compounding= 3750/1.2677 (derieved above) = 2958.023

Thus the amount to be deposited deposited in bank to earn 3750 will be 2958.023.

3. So we should invest in bank deposit as the returns are more in it compared to commercial note. If we dont have alternate investment option we should invest whole 3000 in bank deposit which will fetch 3803.21 at the end of 5 years.