Explanation

Step 1: Understand the bond details

• Par value: $100
• Annual coupon rate: 10%
• Annual coupon payment: 10% × $100 = $10
• Maturity: 10 years
• Holding period: 7 years (sold after receiving 7th coupon)
• Reinvestment rate: 8% annually

Step 2: Calculate future value of reinvested coupons The investor receives 7 annual coupon payments of $10 each, starting at the end of year 1 and ending at the end of year 7. Each coupon is reinvested at 8% until the end of the 7-year holding period.

We need to calculate the future value of an annuity:

• PMT = $10 (annual coupon payment)
• r = 8% (reinvestment rate)
• n = 7 (number of payments)

Step 3: Apply future value of annuity formula The future value of an ordinary annuity formula is: $FV = PMT \times \frac{(1 + r)^n - 1}{r}$

Where:

• PMT = $10
• r = 0.08
• n = 7

$FV = 10 \times \frac{(1.08)^7 - 1}{0.08}$

Step 4: Calculate

1. Calculate (1.08)^7 = 1.713824
2. Calculate (1.713824 - 1) = 0.713824
3. Divide by 0.08: 0.713824 / 0.08 = 8.9228
4. Multiply by $10: 8.9228 × 10 = $89.228

Step 5: Compare with options

• $89.228 is closest to $89.23 (Option C)

Why other options are incorrect:

• Option A ($70.00): This would be the simple sum of 7 coupon payments ($10 × 7 = $70), ignoring reinvestment income.
• Option B ($75.90): This appears to be using an incorrect calculation, possibly using a lower reinvestment rate or incorrect time period.

Key Concept: This question tests understanding of reinvestment risk and the time value of money. When coupons are reinvested, they earn additional interest, increasing the total return beyond just the sum of the coupon payments.