Discounted Promissory note

[petedam]

Here's the question and please help me..

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?

thanks in advance

 

[Denis]

Once more, Pete! :

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.

 

[petedam]

Thanks again Denis. You respond in S.O.S was enough! Greatly appreciated.