Let’s solve the problem step by step: ### **Given:** - **Par value of bond (\( F \)):** $1,000 - **Coupon rate:** 10% *annual*, paid **quarterly** - **Coupon payment per quarter (\( PMT \)):** \( = \$1,000 \times \frac{10\%}{4} = \$1,000 \times 0.025 = \$25 \) per quarter - **Number of years:** 6 - **Number of quarters (\( n \)):** \( = 6 \times 4 = 24 \) - **Investor's required rate (\( i \)):** 8% *annual*, but **per quarter**: \( = \frac{8\%}{4} = 2\% = 0.02 \) per quarter --- ## **Step 1: Identify the Present Value Formula** The price of the bond is the present value (PV) of all coupon payments (an ordinary annuity) **plus** the present value of the par value (a single sum): \[ PV = PMT \times \left[ \frac{1 - (1 + i)^{-n}}{i} \right] + \frac{F}{(1 + i)^n} \] --- ## **Step 2: Plug in the Values** - \( PMT = 25 \) - \( i = 0.02 \) - \( n = 24 \) - \( F = 1000 \) \[ PV = 25 \times \left[ \frac{1 - (1 + 0.02)^{-24}}{0.02} \right] + \frac{1000}{(1 + 0.02)^{24}} \] --- ## **Step 3: Calculate Each Component** ### **A) Present Value of Coupons** First, calculate \( (1 + 0.02)^{-24} \): \[ (1 + 0.02)^{-24} = (1.02)^{-24} \] Calculate \( (1.02)^{24} \): \[ \ln(1.02) = 0.01980 \] \[ 24 \times 0.01980 = 0.4752 \] \[ e^{0.4752} = 1.60776 \] So, \[ (1.02)^{24} = 1.60776 \] \[ (1.02)^{-24} = \frac{1}{1.60776} = 0.62197 \] Now, plug in: \[ PV_{\text{coupons}} = 25 \times \frac{1 - 0.62197}{0.02} = 25 \times \frac{0.37803}{0.02} \] \[ = 25 \times 18.90150 = 472.53750 \] --- ### **B) Present Value of Par Value** \[ PV_{\text{par}} = \frac{1000}{1.60776} = 621.96912 \] --- ### **C) Total Present Value** \[ PV_{\text{total}} = 472.53750 + 621.96912 = 1094.50662 \] --- ## **Step 4: Round Final Answer** Round to the nearest whole number: \[ \boxed{1,095} \] --- ## **Final Answer** \[ \boxed{1,095} \] So, the purchaser would be willing to pay **$1,095** for the bond.