To calculate the price of a zero-coupon bond, we use the formula:

P = F / (1 + r)^n

where:
P = price of the bond
F = face value of the bond
r = yield to maturity (YTM)
n = number of years to maturity

Given in the problem:
F = $100
r = 7% or 0.07
n = 15 years

Substituting these values into the formula, we get:

P = 100 / (1 + 0.07)^15

Now, calculate the value inside the parenthesis:

1 + 0.07 = 1.07

Then, raise this to the power of 15:

1.07^15 = 2.75902

Finally, divide the face value by this number:

P = 100 / 2.75902 = $36.23

So, the price per $100 of face value that the bond will trade at if the YTM is 7% is approximately $36.23.

Question

To calculate the price of a zero-coupon bond, we use the formula:

P = F / (1 + r)^n

where:
P = price of the bond
F = face value of the bond
r = yield to maturity (YTM)
n = number of years to maturity

Given in the problem:
F = $100
r = 7% or 0.07
n = 15 years

Substituting these values into the formula, we get:

P = 100 / (1 + 0.07)^15

Now, calculate the value inside the parenthesis:

1 + 0.07 = 1.07

Then, raise this to the power of 15:

1.07^15 = 2.75902

Finally, divide the face value by this number:

P = 100 / 2.75902 = $36.23

So, the price per $100 of face value that the bond will trade at if the YTM is 7% is approximately $36.23.

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