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

Introduction / Context:
A strip bond is a fixed income security that pays a single lump sum at maturity and no periodic coupons. Its present value is calculated by discounting the face value back to today using the appropriate market yield and compounding convention. This question requires the application of the compound interest formula in reverse: given the future value, yield rate, compounding frequency, and time to maturity, we must find the bond price today. It reinforces both time value of money concepts and careful handling of semiannual compounding.

Given Data / Assumptions:

• Face value (FV) of the strip bond = $10,000.
• Time to maturity = 15 years from today.
• Market rate of return (yield) = 6.5% per annum.
• Compounding is semiannual, so there are 2 compounding periods per year.
• The bond pays no coupons; a single payment of $10,000 is received at maturity.

Concept / Approach:
The present value of a future single sum under compound discounting is:
PV = FV / (1 + i)^nHere, i is the periodic interest rate and n is the total number of periods. For a nominal annual yield of 6.5% compounded semiannually, we have:
i = 0.065 / 2n = 15 * 2 = 30 periodsWe then substitute FV = 10000, i and n into the formula to obtain the fair price of the bond.

Step-by-Step Solution:
Step 1: Compute the semiannual rate: i = 6.5% / 2 = 3.25% per half year, or 0.0325 in decimal form.Step 2: Determine the total number of compounding periods: n = 15 years * 2 = 30 semiannual periods.Step 3: Write the present value formula: PV = 10000 / (1 + 0.0325)^30.Step 4: Calculate the denominator (1.0325)^30 using repeated compounding or a calculator. This gives a value larger than 2, reflecting growth over 15 years.Step 5: Divide 10000 by this factor. Numerically, the result is approximately PV = 3830.88.Step 6: Therefore, the fair market value of the strip bond is about $3830.88.

Verification / Alternative check:
We can check reasonableness. A 6.5% annual yield compounded semiannually over 15 years implies more than doubling, but less than quadrupling, of a sum. If we move from present to future, 3830.88 growing for 30 periods at 3.25% per period should yield roughly 10000. That is, 3830.88 * (1.0325)^30 ≈ 10000. This reverse multiplication confirms that 3830.88 is a suitable discounting result, so the calculation is consistent.

Why Other Options Are Wrong:
$1710.29 and $2710.29 are too low, suggesting an unrealistically high effective yield. $4710.29 and $5200.00 are too high, corresponding to yields lower than the given 6.5% per annum. Only $3830.88 satisfies the correct present value formula using a 6.5% nominal annual yield with semiannual compounding for 15 years.

Common Pitfalls:
Common mistakes include using the annual rate of 6.5% directly as i without dividing by 2, or using n = 15 instead of 30, which mixes annual and semiannual compounding incorrectly. Another error is to multiply instead of divide by (1 + i)^n when discounting, confusing present value with future value. Carefully identifying whether we are moving from future to present or from present to future helps avoid such errors.

Final Answer:
The fair present value of the $10,000 face value strip bond with 15 years to maturity at 6.5% per annum compounded semiannually is approximately $3830.88.