Question

Ace Co. sold King Co. a $20,000, 8%, 5-year note that required five equal annual year-end payments. This note was discounted to yield a 9% rate to King. The present value factors of an ordinary annuity of $1 for five periods are as follows:

Answer 1

Answer:

$5,560

Explanation:

One thing of note in this question is the annual payment needed to pay the note. Why, the note yields a higher rate (9%) than it pays (8%), the note should have a discount. Since the note has a stated rate of 8%, the annual payments will be based on the present value of an ordinary annuity based on the 8%: Thus, the annual payment is $20,000 ÷ 3.993, or $5,009 annually.

The PV of the note, however, and thus the initial discount is based on the yield percentage of 9%. Therefore, the note's initial present value is the payment amount multiplied by 3.89 ($5,009 × 3.89), or $19,485.

The sum of interest revenue a person earns on a note is related to the total payments and also the PV of the note, with a discount recognized here initially, on this note. The total amount to be received on this note is 5 × $5,009, for a total of $25,045.

Interest is generally the amount returned over and above the amount originally recognized, which was the $19,485 originally. Thus, the total interest revenue is $25,045 − $19,485, or $5,560.