A promissory note has a face value of $5000 and it carries an interest rate of 5% for a period of 6 months (including the period of grace). It is sold 3 months before the legal due date. What is the present value of the note on the date of sale if money is worth 4%?
A) $5047.26
B) $5070.26
C) $5074.26
D) $5125.00
E) $5125.26

Question

Quizplus · Accepted Answer

The present value of the note can be calculated using the formula for the present value of a future amount: $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the interest rate per period, and $n$ is the number of periods. First, calculate the future value of the note including interest for 6 months at 5% per annum: $FV = 5000 \times (1 + 0.05 \times \frac{6}{12}) = 5000 \times (1 + 0.025) = 5000 \times 1.025 = 5125$. Then, calculate the present value of this amount 3 months before its due date at an interest rate of 4% per annum: $PV = \frac{5125}{(1 + 0.04 \times \frac{3}{12})} = \frac{5125}{(1 + 0.01)} = \frac{5125}{1.01} = 5074.257$, which rounds to $5074.26.

A Promissory Note Has a Face Value of $5000 and It