Question

Suppose someone offered to sell you a note calling for payment of $1,225 15 months from today (456 days). They offer to sell it to you for $950. You have $950 in a bank time deposit which pays a 12% nominal rate with a daily (365 days a year) compounding, and you plan to leave the money in the bank unless you buy the note? Recommend action based on checking 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

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

the future value of the note = $1,225

the future value of the time deposit = $950 x (1 + 0.12/365)⁴⁵⁶ = $1,103.62

the note has the highest future value

(2) by comparing the PV of the note with your current bank account, and

PV of note = $1,225 / (1 + 0.12/365)⁴⁵⁶ = $1,054.48 (I used the same interest rate than the time deposit)

present value of your time deposit = $950

the note has the highest present value

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

EAR of the note using the future value formula:

1,225 = 950 x (1 + r)¹°²⁵

(1 + r)¹°²⁵ = 1,225 / 950 = 1.2895

¹°²⁵√(1 + r)¹°²⁵ = ¹°²⁵√1.2895

1 + r = 1.2255

r = 0.2255 = 22.55%

EAR time deposit = (1 + 0.12/365)³⁶⁵ - 1 = 12.75%

the note's effective annual rate is higher