Explanation

The correct answer is B (99.96) because:

Backward Induction Calculation:

1. Calculate Time 1 bond values including coupon:

   • Upper node: 99.715 + 2.0 = 101.715
   • Lower node: 100.247 + 2.0 = 102.247

2. Discount back to Time 0 using current 1-year spot rate:

   • Average of Time 1 values: (101.715 + 102.247) / 2 = 101.981
   • Discount factor: 1 / (1 + 0.015) = 0.98522
   • Present value: 101.981 × 0.98522 = 100.47

3. Adjust for current coupon payment:

   • Since this is an annual coupon bond, we need to add the current coupon payment to get the full bond value
   • Final bond value: 100.47 + 2.0 = 102.47

Wait, let me recalculate this properly:

Correct Calculation:

1. Calculate Time 1 bond values (already given):

   • Upper node: 99.715
   • Lower node: 100.247

2. Add coupon payment at Time 1:

   • Upper node: 99.715 + 2.0 = 101.715
   • Lower node: 100.247 + 2.0 = 102.247

3. Discount back to Time 0 using current 1-year spot rate (1.5%):

   • Average of Time 1 values: (101.715 + 102.247) / 2 = 101.981
   • Discount factor: 1 / (1 + 0.015) = 0.98522
   • Present value: 101.981 × 0.98522 = 100.47

4. Add current coupon payment at Time 0:

   • Since the bond pays annual coupons, we need to add the coupon payment that occurs at Time 0
   • Final bond value: 100.47 + 2.0 = 102.47

However, looking at the options, 99.96 is closest to the calculation without adding the current coupon. Let me verify:

Actually, the backward induction method typically gives the bond value directly. Let me recalculate:

Proper Backward Induction:

At Time 2, the bond matures and pays principal + coupon = 100 + 2 = 102

At Time 1:

• Upper node: PV = (102 / (1 + 0.02292)) = 99.715 ✓
• Lower node: PV = (102 / (1 + 0.01749)) = 100.247 ✓

Now at Time 0:

• Average of Time 1 values: (99.715 + 100.247) / 2 = 99.981
• Add coupon payment at Time 1: 99.981 + 2.0 = 101.981
• Discount to Time 0: 101.981 / (1 + 0.015) = 100.47

But this gives 100.47, which is option C.

Wait, let me check the calculation again:

Final Correct Calculation:

At Time 1, the bond values are:

• Upper node: 99.715
• Lower node: 100.247

These values already include the Time 2 cash flows discounted back. Now we need to:

1. Add the coupon payment at Time 1 to each node:

   • Upper: 99.715 + 2.0 = 101.715
   • Lower: 100.247 + 2.0 = 102.247

2. Calculate the average: (101.715 + 102.247) / 2 = 101.981

3. Discount to Time 0 using 1.5%: 101.981 / 1.015 = 100.474

This gives 100.47, which matches option C.

However, the question says "closest to" and the options are 98.50, 99.96, and 100.47. Since 100.47 is an exact match to option C, that should be the correct answer.

Therefore, the correct answer is C (100.47).