1. **State the problem:** Calculate the price of a bond with face value $10,000$, annual coupon rate 5%, 4 years to maturity, and current market interest rate 6%. 2. **Formula for bond price:** The price of a bond is the present value of its future coupon payments plus the present value of the face value at maturity: $$\text{Price} = \sum_{t=1}^N \frac{C}{(1+r)^t} + \frac{F}{(1+r)^N}$$ where: - $C$ = annual coupon payment - $r$ = market interest rate (yield to maturity) - $F$ = face value - $N$ = number of years to maturity 3. **Calculate coupon payment:** $$C = 10,000 \times 0.05 = 500$$ 4. **Calculate present value of coupons:** $$\sum_{t=1}^4 \frac{500}{(1+0.06)^t} = 500 \times \left(\frac{1 - \frac{1}{(1.06)^4}}{0.06}\right)$$ 5. **Calculate present value of face value:** $$\frac{10,000}{(1.06)^4}$$ 6. **Calculate each term:** $$\frac{1}{(1.06)^4} = \frac{1}{1.2625} \approx 0.7921$$ 7. **Calculate present value of coupons:** $$500 \times \frac{1 - 0.7921}{0.06} = 500 \times \frac{0.2079}{0.06} = 500 \times 3.465 = 1732.5$$ 8. **Calculate present value of face value:** $$10,000 \times 0.7921 = 7921$$ 9. **Calculate bond price:** $$1732.5 + 7921 = 9653.5$$ **Final answer:** The price of the bond is approximately $9653.5$.