[SuperAccountingGod]

“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?”
ANSWER: 5,560
SOLUTION: 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.”

The issue I have with this is how they got the payment of $5009. I’m used to multiplying the stated rate times the face amount to get the payment, yet here they divide. The problem stated 5 equal payments so I tried dividing the $20K by 5 years and got a payment of $4K but that wasn’t right either. I’m just not a fan of how there are so many different ways to solve these types of problems and you have to read between the lines to just know how to approach these. So I guess my question is why do they divide instead of taking the stated rate of 8% and multiplying it by the $20k?

[chandler]

Because this is an annuity (loan) where principal is paid back over time with interest in each payment. Stated rate* balance only works for interest-only applications (bonds).
– You use the stated rate PV factor to figure out the payment amount ($5,009), but the discounted rate PV factor to figure out sell price of the note ($19,845).
-I'm wondering if you are not seeing the full scope of this transaction. Really, making the loan and selling it are two distinct transactions you have to account for somewhat separately.

[SuperAccountingGod]

So if it is interest only payments, then stated rate * principle, and principle + interest payments, then principle/PVOA? I think I see that concept now. But I don't see how that is being asked in this specific question as all it says is equal annual payments and provides the PVOA factors.
I think the other issue that is confusing me is being able to ascertain when an amount is the face amount or the PV. Because I thought the $20K was the face value but apparently it is the PV. How can you tell when an amount is the face value or the PV? I think once I figure that out everything else will fall in place.

[Author]

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