[TNTTN]

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% 3.992
9% 3.890
What should be the total interest revenue earned by King on this note?
A. $9,000
B. $8,000
C. $5,560
D. $5,050
Explanation
Choice “C” is correct. $5,560 total interest revenue.
Annual payments = $20,000 ÷ 3.992 = $ 5,010
Five equal payments of principal and interest.
Total payments = $ 5,010 x 5 = $25,050
Discounted note = $5,010 x 3.890 = (19,490)
Total interest over five years
$ 25,050 – $ 19,490 = $ 5,560

I’m so confused why we divide the PV factor to find the total payments?
I thought it should be like this:
Total payment/Maturity value of the note
= PV of Face value + PV of total interest payments
= $20,000 x 3.890 + $20,000 x 8% x 3.890 = $84,084

[Asja]

Wow! I was stuck on the same question, like RIGHT NOW!!I almsot posted about it. No way!…This is Surgent..They don't fully explain some things…I really hate the stupid charts…Honestly, I want to use my financial calculator…I'm gonna perform an autopsy on this animal and then get back to you.

[Asja]

Okay you are saying it should be like = $20,000 x 3.890 + $20,000 x 8% x 3.890 = $84,084

I just calculated things my way – whatever way you know how to calculate PV of annuity and payments…

So…The note is purchased at a discount, and that discount is calculated by figuring out the PV of the equal payments (annuity)…For that we would use the yield rate of 9%…but we need to know what those equal payments are first…

The payments are done using 8% rate…

So calculate the 5 payments over the 5 years…which you do with PV as -20,000 and FV as ZERO, you just plug in the n=5 and rate=8%…and compute the payment…which is 5009…

Then the present value of the 5009 for five years at the rate of 9% is 19,485…that is the cash outlay to buy the note…

so total return is 5009*5=25045
less 19485 of PV paid initially
is $5,560 interest earned (so the discount is essentially considered interest earned as well I guess)

I assume I didn't help at all…sorry

[TNTTN]

I think I sort of get it. Correct me if I'm wrong.

Interest revenue = FV/maturity of the note – PV of the note

Firstly, to calculate the FV/maturity value of the note, we can use the FV of ordinary annuity formula which = Annual payment x FV factor of a ordinary annuity. However, the FV factor of an ordinary annuity is not given, thus, FV/maturity value of the note = Annual payment x 5 payments . So, basically there are 2 ways to calculate the FV/maturity value of a note?

Secondly, regarding the PV of the note, I thought Total payment/Maturity value of the note = PV of Face value + PV of total interest payments, and it is incorrect because unlike bonds (interest is paid several times, principal is paid once at the end of the bond term), each note payment includes both principal and interest. Therefore, PV of the note = Annuity payment x PV factor of an ordinary annuity/annuity due depending on the question. The fact gave us the PV of the note of $20,000, but we cannot use that amount because that is discounted at 8%. We need to find a new PV of the note when it is discounted at 9%. Since, the PV factor of an ordinary annuity is given, the PV of the note = PV of ordinary annuity = Annuity payment x PV factor of an ordinary annuity. In my initial post,

So the key here is to find how much the annual/annuity payment is when the note is discounted at 9%. So, annuity payment = PV of ordinary annuity / PV factor of an ordinary annuity = $20,000 / 3.992 = $5,010
Now, we just plug this number to the formulas.

FV/maturity value of the note discounted at 9% = Annual payment x 5 payments = $5,010 x 5 = $25,050
PV of the note discounted at 9% = Annuity payment x PV factor of an ordinary annuity = $5,010 x 3.890 = $19,490
=> Interest revenue = FV/maturity of the note – PV of the note = $25,050 – $19,490 = $5,560

Am I right????????? 🙁

[Author]

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