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# Math Help Needed

United StatesPosts: 3 Associate
Alright, I cannot figure out all of the steps to get the answer to a problem shown in Reading 36, page 128 of Level 2 in the physical book copy.

The bottom of the page is showing steps to solve for a Spot Rate from a Par Rate. Specifically, it's a 2 year spot rate that we are trying to solve. Any help is greatly appreciated to show all steps to isolate the 2 yr Spot Rate and get the answer they show of 3.008.

Par = 100
Par Rate = 3%
N = 2 yearly payments
1 Yr Par Rate =2.500%
2 Yr Spot Rate = ??

3/1.025 + 103 / (1 +r) ^2 = 100

I get that 3/1.025 = 2.9268

Then subtracting 2.9268 from both sides gives:

103 / (1+r)^2 = 97.0732

From this point on I get stuck on the exact steps to isolate and solve for r.
Tagged:

• 103 / (1+r)^2 = 97.0732
103 / 97.0732 = (1+r)^2
1.0611 = (1+r)^2
(1.0611)^(1/2) = 1+r
1+r = 1.0301
r = 0.0301
r = 3.01%
• United StatesPosts: 3 Associate
Thanks for responding... For the 2nd line you're showing: 103/97.07 = (1+r)^2. I'm still a little confused. How did you get this line? I "thought" that you would have to multiply both sides by ((1+r)^2) / 1 to arrive at 103 (1+r)^2 = 97.07 (1+r)^2. But I know that's not right.
• OKPosts: 9 Associate
Multiply both sides by (1+r)^2. That will get you to => 103*(1+r)^2 / (1+r)^2 = 97.0732*(1+r)^2. The (1+r)^2 term on the left cancels out. And then you divide both sides by 97.0732.

Once you get there you take the square root of both sides to get rid f the square term and subtract 1 from both sides. Leaves you with "r = ......"
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