1. **State the problem:** We are given a bond with face value $1000$, current price $950$, annual coupon rate 4%, and maturity 4 years. We need to find: (i) Current yield (ii) Yield to maturity (YTM) 2. **Formulas and explanation:** - Current yield is calculated as the annual coupon payment divided by the current price: $$\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Price}}$$ - Yield to maturity (YTM) is the interest rate $r$ that satisfies the equation: $$950 = \sum_{t=1}^4 \frac{40}{(1+r)^t} + \frac{1000}{(1+r)^4}$$ where $40 = 4\% \times 1000$ is the annual coupon payment. 3. **Calculate current yield:** Annual coupon payment = $1000 \times 0.04 = 40$ $$\text{Current Yield} = \frac{40}{950} \approx 0.0421 = 4.21\%$$ 4. **Calculate yield to maturity (YTM):** We solve for $r$ in: $$950 = \frac{40}{(1+r)} + \frac{40}{(1+r)^2} + \frac{40}{(1+r)^3} + \frac{40}{(1+r)^4} + \frac{1000}{(1+r)^4}$$ This is a nonlinear equation and typically solved by trial, interpolation, or financial calculator. 5. **Approximate YTM by trial:** Try $r=5\%$: $$\text{Price} = \frac{40}{1.05} + \frac{40}{1.05^2} + \frac{40}{1.05^3} + \frac{40}{1.05^4} + \frac{1000}{1.05^4} \approx 38.10 + 36.29 + 34.56 + 32.91 + 822.70 = 964.56$$ Price is higher than 950, so try higher $r$. Try $r=6\%$: $$\text{Price} = \frac{40}{1.06} + \frac{40}{1.06^2} + \frac{40}{1.06^3} + \frac{40}{1.06^4} + \frac{1000}{1.06^4} \approx 37.74 + 35.59 + 33.56 + 31.64 + 792.09 = 930.62$$ Price is lower than 950, so YTM is between 5% and 6%. 6. **Interpolate linearly:** $$r \approx 5\% + \frac{964.56 - 950}{964.56 - 930.62} \times (6\% - 5\%) = 5\% + \frac{14.56}{33.94} \times 1\% \approx 5.43\%$$ **Final answers:** (i) Current yield $\approx 4.21\%$ (ii) Yield to maturity $\approx 5.43\%$