A $10,000 face value strip bond has 15 years remaining until maturity. If the prevailing market rate of return is 6.5% per annum compounded semiannually, what is the fair present market value (price) of this strip bond?

Introduction / Context:
A strip bond (zero coupon bond) pays no periodic coupons. Instead, the investor receives a single lump sum equal to the face value at maturity. The fair price today is the present value of that future payment discounted at the market yield, taking into account the compounding frequency.

Given Data / Assumptions:

Face value (future value) F = $10,000.
Time to maturity t = 15 years.
Market rate of return r = 6.5% per annum nominal, compounded semiannually.
Compounding frequency m = 2 times per year.
We are pricing a zero coupon bond, so there are no intermediate cash flows.

Concept / Approach:
For a nominal rate r compounded m times per year, periodic rate i = r / m. The number of compounding periods n = m * t. The present value PV of a future amount F is: PV = F / (1 + i)^n We plug in F = 10,000, i = 0.065 / 2 and n = 2 * 15 = 30.

Step-by-Step Solution:
Step 1: Find the periodic rate. i = 6.5% / 2 = 3.25% per half year = 0.0325. Step 2: Find the total number of periods. n = 15 years * 2 = 30 semiannual periods. Step 3: Apply the present value formula. PV = 10,000 / (1.0325)^30. Numerically, this is approximately PV ≈ $3,830.88.

Verification / Alternative check:
You can check the reasonableness: over 15 years at roughly 6.5% compounded semiannually, the future value of $3,830.88 would grow to about $10,000. This is consistent with the concept that the present value is the discounted equivalent of the future payment at the market yield.

Why Other Options Are Wrong:
$3,710.29 and $3,500.00 are too low and would correspond to higher effective yields than 6.5%, making the bond underpriced relative to the stated market rate. $4,000.00 is too high and would imply a lower yield than 6.5%. Only $3,830.88 matches the correct discounting at 6.5% compounded semiannually.

Common Pitfalls:
Students sometimes discount using simple interest or forget to adjust the annual rate for the semiannual compounding, using 6.5% per period instead of 3.25%. Others mistakenly treat the bond as if it pays coupons, though the word 'strip' indicates a single lump sum at maturity. Always match the compounding frequency to the rate and the number of periods.

Final Answer:
The fair present market value of the strip bond is approximately $3,830.88.