Question

Peter has a bond that has a face amount of $1000 and will mature in 15 years. The nominal interest rate is 9%. What is the price of the bond that will yield an effective interest rate of 8%?

Answer 1

You have some arithmetic before you.

There are 30 coupon payments of 1000 * 0.09 / 2 = 45
There is one final payment of $1000 at 15 years.

i = 0.04
j = i/2 = 0.02
v = 1/(1+j)

Building from basic principles

Price = 45(v + v^2 + v^3 + ... + v30) + 1000v^30

Or

\(Price = 45\dfrac{v-v^{31}}{1-v} + 1000v^{30} = 45\dfrac{1-v^{30}}{j} + 1000v^{30}\)

If you can learn to do this fluently, you will ace this course!! Others will still be trying to remember the right formula!! Building them on the fly from basic principles is the way to go.

Answer 2

How did you get the geometric progression? Where did the i come from?

Answer 3

the i is 9% and 8%...does it is corect...with the question...

Answer 4

how you get i=0.04

Answer 5

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Answer 6

The nominal rate is given, 9%. This would normally motivate the semi-annual coupon most common with U.S. Bonds.

The required investment return is 8% and is given in the problem statement. Calculating semi-annually, because that's when the coupons hit, gives j = 0.04. Sorry, that was in error up above. It should be i = 0.08 and j = 0.04.

The geometric series is a natural consequence of the equally spaced cash flows. The first is discounted 0.5 years (v), the second is discounted 1.0 years (v^2), etc. Remember that v is designed specifically so that it would be semi-annual.

i, j, v, etc. These are definitions stated pretty clearly (although incorrectly in the original post.) I don't get them from anywhere, I define them.

Answer 7

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**** JUST TO EMPHASIZE AND CORRECT MY ERROR ****
*********************************************************

Two of the interest rate definitions given above are incorrect. They should have been as follows:

i = 0.08 - The required annual investment return.
j = 0.04

This does not affect the construction of the necessary formula.

Many apologies for the error. Typing too quickly too early in the morning, I think.

Answer 8

Thanks

Answer 9

Thanks alot.