Find the Yield Rate of Two Bonds with Same Maturity & Coupon Rate

[SciFi Chick]

"One bond, with a face value of 1000 dollars and annual coupons at a rate of 7.2 percent effective, has a price of 1001.99 dollars. A second bond, with a face value of 1000 dollars and annual coupons at a rate of 6 percent effective, has a price of 882.83 dollars. Both bonds are redeemable at par in the same number of years, and have the same yield rate. Find the yield rate. (Give your answer as an effective rate.)"

The formula we are supposed to work with is along these lines:

1001.99=(1000*.072)(1+Y)^-n/Y + 1000(1+Y)^-n

I've been looking at this problem for five hours, and I cannot think of a way to solve it. I would imagine that the fact that the two bonds have the same number of years and the same yield rate is significant, but I can't figure out why. This class does not teach theory, only formulas. Please help.

 

[Oxymoron]

First, do you have Maple (or some other maths software package)?

 

[SciFi Chick]

No. But after much agony and banging of my head against the wall, I was able to figure it out. Thanks!

I'm sure I'll be back in the summer when I have Calculus.

 

[Oxymoron]

what did you get?

 

[SciFi Chick]

My apologies for the belated reply. I found help from a friend, who suggested I substitute x for (1+Y)^-n. From there, it's a simple matter of using the substitution method on the two equations, and since all I need is the solution to Y, it's not necessary to solve for -n.

The answer turned out to be 7.18% for the yield rate.