Hi everyone,
As elementary as this might be (in all honesty, I’m not sure if it is), could someone please shed some light on how you actually solve for “r” mathematically in Question 31 of reading 53? Any assistance or discussion would be greatly appreciated!
It isn’t.
Because you have four payments to discount, you end up with a 4th-degree polynomial in r. You can use Ferrari’s method, Descarte’s method, or other methods to find the roots of this polynomial, but in practice, nobody ever does this; they simply use numerical methods to find an approximation to a root.
If you have more than 4 payments, then you have to use numerical methods; Galois proved this.
Hi S2000magician,
Thank you for clarifying. I’ve done a bit of reading up on the items you mentioned and have concluded that a question similar to this in the level 1 exam is unlikely. Hoping that’s a fair assessment because my mathematical ability isn’t quite where it needs to be to get this right!
You likely won’t get such a question.
However, if you do, realize that you don’t need to solve for r; CFA Institute will already have done that for you and included the correct answer in one of the answer choices: a , b , or c.
If they ask you such a question, bearing in mind that the answer choices for r will be listed from smallest to largest, you need only to check answer b. If that value of r gives you today’s price on the bond, then b’s the correct answer. If it gives you a price that is too low, then that value of r is too high: a is the correct answer; if it gives you a price that is too high, then that value of r is too low: c is the correct answer.