Help Me Solve For Bond Ytm!

[Starcreator]

Can anyone solve for "r" in the following formula? None of my math teacher could.

950 = (50 / (1+R)^2) + (50 / (1+R)^1) + (1000 / (1+R)^2)

For thosee who are concerned, it is a calculation of bond present value and YTM.

[Afterburner]

if r has to be positive it is 0.07796. (approximately)

[Afterburner]

if r is negative then it is -2.205328484 etc.

[Diamond187]

By algebra I get it down to -3=22r+r^3

[Afterburner]

Lol, you screwed up man...there is no r^3 in the whole thing, it can't happen

my answers are right trust me...just plug them back in

[Liokae]

Is algebraic proof required, or merely values?

[Diamond187]

ummm, try getting a common denominator without an r^3

note: from now on I'm typing in maple and pasting into my replies so I can read my math

[Liokae]

ummm, try getting a common denominator without an r^3

note: from now on I'm typing in maple and pasting into my replies so I can read my math


The LCD is (1+r)^2, bright one.

Anywho, the algebraic proof:

950 = (50/(1+r)^2) + [((1+r)50)/(1+r)^2] + 1000/(1+r)^2

950 = [(50 + 50 + 50r + 1000)/(1 + r)^2]

950 = [(50r + 1100)/(r^2 + 2r + 1)]

950r^2 + 1900r + 950 = 50r + 1100

950r^2 + 1850r = 150

19r^2 + 37r = 3

19r^2 + 37r - 3 = 0

And from there you can use the quadratic formula to get your values. Doing so, we get...

r = [(-37 (+/-) sqrt(37^2 -4(10)(-3)))/(2 * 18 )]

r = [(-37 (+/-) sqrt(1369 + 228))/38]

r = (-37 (+/-) sqrt(1597)) / 38

r = [.0779, -2.625]

[Afterburner]

liokae's right...and the answers you get are the two i listed above

[jason]

uh... i am confused :| well i m in grade 7 so i m stupid.......

[Diamond187]

LOL
i misread it
i thought it was 1/(1+r^2)

So, the final exact answers are -37/38+1/38*sqrt(1597), -37/38-1/38*sqrt(1597)

Blar! Maple doesn't post right!

[Starcreator]

Well r is equal to afterburners answr but I still don't see how many people get it here's how i get it down to this is my latest step

950 x (1+R)^2 = 50 + 50DR + 1000

[Diamond187]

Well, then you set it up in quadratic form
(ax^2+bx+c=0) and use the quadratic formula to solve. (That D is typo, right?)

[Afterburner]

It's very simple. This is my process:

Add the 50/(1+R)^2 and the 1000/(1+R)^2 together, since they have a common denominator.

Multiply the top/bottom of the other fraction by 1+R, then add that to the other sum.

Multiply across, simplify, and use the quadratic formula.

[Liokae]

Which is, naturally, what's already been done.

[Afterburner]

sorry about that, didn't read the whole thing

[Starcreator]

I've got it now....and yeah that D was a typo