# Discounted Promissory note

• Jun 30th 2010, 09:58 AM
petedam
Discounted Promissory note

A five (5) year promissory note for \$1,000, bearing interest at 9% compounded annually, was discounted at 12% compounded semi-annually yielding proceeds of \$1,416.56.

1. What was the amount of the compound discount?

EDIT: Am I suppose to find FV and subtract the proceeds from it?
• Jul 2nd 2010, 06:30 AM
Wilmer
Whoever holds that promissory note is guaranteed to receive
1000(1.09^5) = 1538.62 at the maturity date of the note.

If someone "bought" that note for 1416.56 and will earn 12% cpd semi-annually,
then he MUST have bought it a bit before maturity date; in other words, 1416.56
at this rate for some period of time T accumulates (has future value) of 1538.62

SO: 1416.56(1.06)^T = 1538.62
Solving for T gives ~1.4185... or 1.42 (rounded) semi-annual periods.

1.42 semi-annual periods = 8.5 months (rounded).
So purchase made after 4 years and 3.5 months: 4.29 years

1000(1.09)^4.29 = 1447.30 ; so:
1447.30 - 1416.56 = 30.74 ... which is the discount amount.

Above by Wilmer, discounter extraordinaire :)
• Jul 2nd 2010, 08:44 AM
petedam
Thank you very much!
• Jul 4th 2010, 06:25 PM
petedam
Quote:

Originally Posted by Wilmer
Whoever holds that promissory note is guaranteed to receive
1000(1.09^5) = 1538.62 at the maturity date of the note.

If someone "bought" that note for 1416.56 and will earn 12% cpd semi-annually,
then he MUST have bought it a bit before maturity date; in other words, 1416.56
at this rate for some period of time T accumulates (has future value) of 1538.62

SO: 1416.56(1.06)^T = 1538.62
Solving for T gives ~1.4185... or 1.42 (rounded) semi-annual periods.

1.42 semi-annual periods = 8.5 months (rounded).
So purchase made after 4 years and 3.5 months: 4.29 years

1000(1.09)^4.29 = 1447.30 ; so:
1447.30 - 1416.56 = 30.74 ... which is the discount amount.

Above by Wilmer, discounter extraordinaire :)

Just letting you know..the answer should be as follow as told by my instructor

i = j/m = 9%/1 = 9%
n = 5
FV = PV(1 + i)n
= \$1,000(1 + .09)5
= \$1,538.62
Compound discount = \$1,538.62 - \$1,416.56 = \$122.06
• Jul 4th 2010, 07:26 PM
Wilmer
Quote:

Originally Posted by petedam
Just letting you know..the answer should be as follow as told by my instructor
i = j/m = 9%/1 = 9%
n = 5
FV = PV(1 + i)n
= \$1,000(1 + .09)5
= \$1,538.62
Compound discount = \$1,538.62 - \$1,416.56 = \$122.06

Ok then, could you ask that instructor of yours to define "compound discount".
IF what you posted is correct, he HAS to tell you:
"compound discount means the future value of the original note less the proceeds from selling the note"

...which is really silly, and really means "nothing", except a simple future value calculation.
• Jul 4th 2010, 07:36 PM
petedam
"compound discount means the future value of the original note less the proceeds from selling the note"

A five (5) year promissory note for \$1,000, bearing interest at 9% compounded annually, was discounted at 12% compounded semi-annually yielding proceeds of \$1,416.56.

yes that's what she did...she figured out the FV and subtracted the proceeds from selling the note.
• Jul 5th 2010, 02:22 AM
Wilmer
Quote:

Originally Posted by petedam
yes that's what she did...she figured out the FV and subtracted the proceeds from selling the note.

Ya...so the problem boils down to a simple subtraction of really 2 given amounts:

GIVEN: A five (5) year promissory note for \$1,000, bearing interest at 9% compounded annually, ...
That's 1538.62
GIVEN: was discounted at 12% compounded semi-annually yielding proceeds of \$1,416.56.
That's 1416.56

1538.62 - 1416.56 = 122.06

I see no real "purpose" here...
• Jul 5th 2010, 06:02 AM
petedam
Quote:

Originally Posted by Wilmer
Ya...so the problem boils down to a simple subtraction of really 2 given amounts:

GIVEN: A five (5) year promissory note for \$1,000, bearing interest at 9% compounded annually, ...
That's 1538.62
GIVEN: was discounted at 12% compounded semi-annually yielding proceeds of \$1,416.56.
That's 1416.56

1538.62 - 1416.56 = 122.06

I see no real "purpose" here...

The purpose is to trick you and it did tricked me. Originally that's what i thought i had to do. Have a look at my original question.

"EDIT: Am I suppose to find FV and subtract the proceeds from it? "
• Jul 5th 2010, 09:40 AM
Wilmer
Quote:

Originally Posted by petedam
"EDIT: Am I suppose to find FV and subtract the proceeds from it? "

Dunno. I give up! Ask that "instructor?" of yours!
• Jul 5th 2010, 09:44 AM
petedam
Quote:

Originally Posted by Wilmer
Dunno. I give up! Ask that "instructor?" of yours!

No I am not asking you any more question the quote in red was part of my original post. :) which turns out to be the way it should have been calculated "according" to my instructor.