# Math Help - bond question

1. ## bond question

Here's a question from an actuarial CAS Exam 2. Can someone show me how to do it. I know the answer is (A), but I'm not sure why.

A 30-year bond has 10% annual coupons and a par value of 1000. Coupons can be reinvested at a nominal annual rate of 6% convertible semi-annually. X is the highest price that an investor can pay for the bond and obtain an effective yield of at least 10%

Calculate X.

(A) 518

(B) 618

(C) 718

(D) 818

(E) 918

2. I figured this out, but I have another question.

A $1000 10% bond has semi-annual coupons. It is purchased new at$880 and is redeemable at $1020. Find the coupon amount and the effective yield rate per coupon period. Can this problem be solved for the effective yield rate? Don't I need the number of coupon periods? The coupon amount is easy (just Fr = (1000)(0.05)), but can I answer the second half as is? 3. Originally Posted by BrainMan I figured this out, but I have another question. A$1000 10% bond has semi-annual coupons. It is purchased new at $880 and is redeemable at$1020. Find the coupon amount and the effective yield rate per coupon period.

Can this problem be solved for the effective yield rate? Don't I need the number of coupon periods? The coupon amount is easy (just Fr = (1000)(0.05)), but can I answer the second half as is?
Is the term of the bond given to you?

4. No it isn't, right? Don't I need the length of the bond to answer the question?

5. Originally Posted by BrainMan
No it isn't, right? Don't I need the length of the bond to answer the question?
I would think so. Using Basic Formula, Premium/Discount, Base Price, and Makeham's, all of them have the term and yield as variables. Do you have Kellison's "Theory of Interest" Book? If not, let me check my copy to see what they say about solving for yield rate and n as well.

Do they want an answer in numerical terms, or in terms of a variable. I remember taking the actuarial exams years ago and one of the bond questions had multiple choices like the question you asked and all the answers were stated in terms of a variable.

Let me know what you think.

I have this lesson here built from Kellison's book on bond pricing, but it's not built to solve for 2 unknowns:

Bond Price Formulas

I know Kellison has another chapter on bonds with respect to yield rates. I'll take a look for you.

6. Thank you very much for helping; I'm pretty sure though you can't answer it as given.

7. Originally Posted by BrainMan
Thank you very much for helping; I'm pretty sure though you can't answer it as given.
Brain Man,

I know we discussed this thread last week, but should you revisit or need to determine yield rates, I built a new lesson if you want to check your work.

Bond Yield Rate Formulas

If redemption value is not stated, just enter the par value for that as well. Let me know if you have questions. Also, if you want the Newton-Raphson approximation built, I can do that by request.