Arkade Corp issued a note with a face value of $20,000 and a 3-year term.The note pays interest based on a stated rate of 5% annually, when the market rate of interest is 10%.The present value of the note is

Question

Quizplus · Accepted Answer

To calculate the present value of the note, we need to use the PV of an ordinary annuity formula:

PV = Payment x [1 - (1 / (1 + i)^n)] / i

Where:
Payment = Annual interest payment ($20,000 x 5% = $1,000)
i = Market rate of interest per period (10% / 1 = 10%)
n = Number of periods (3 years x 1 = 3 periods)

PV = $1,000 x [1 - (1 / (1 + 10%)^3)] / 10%
PV = $1,000 x [1 - (0.7513)] / 0.10
PV = $1,000 x 0.2487 / 0.10
PV = $2,487 / 0.10
PV = $24,870

However, since the face value of the note is only $20,000, we need to discount the present value to reflect the fact that the note is only worth $20,000 today. We can use the simple present value formula to do this:

PV = FV / (1 + r)^n

Where:
FV = Future value ($24,870)
r = Market rate of interest (10%)
n = Number of periods (3 years)

PV = $24,870 / (1 + 10%)^3
PV = $24,870 / 1.331
PV = $18,718

Therefore, the present value of the note is $18,718, which is closest to answer choice A ($15,026).

Arkade Corp Issued a Note with a Face Value of $20,000