Ace Co. sold to 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:
8%: 3.993
9%: 3.890
What should be the total interest revenue earned by King on this note?
A.
$9,000
B.
$8,000
$5,560
D.
$5,050
You are correct, the answer is C.
Explanation: The first thing one needs to answer this question is the annual payment needed to pay the note. Because 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 present value 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 total amount of interest revenue one earns on a note is related to the total payments and also the present value 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.
I wanted to know the way I derived to the answer is also correct or not. I got the same answer as well.
My Calculation: 20,000 x 3.890 = $77,800/5 years = $15,560. Total Interest revenue = $20,000-15,560 = $5560.
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