A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly. What amount was paid for the note?
A) $3500
B) $5978.51
C) $4336.93
D) $6021.50
E) $4251.71

Question

Quizplus · Accepted Answer

First, we need to find the future value of the note after 21 months. Using the formula for compound interest, we have:

FV = PV x (1 + r/n)^(nt)
FV = $3500 x (1 + 0.11/2)^(2/12 x 21)
FV = $4033.17

Next, we need to find the present value of the note at a quarterly interest rate of 2.5% (10% divided by 4). Using the formula for present value, we have:

PV = FV / (1 + r/n)^(nt)
PV = $4033.17 / (1 + 0.1/4)^(4/12 x 2)
PV = $3636.93

Therefore, the amount paid for the note was $3636.93, which is closest to option C ($4336.93).

A Five-Year Promissory Note with a Face Value of $3500