Hoffman Inc. has an $1,000 par value bond with 15 years to maturity and a coupon rate of 12%, paid semiannually. The market rate on similar debt has now risen to 16%. What is the current price of this bond?

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The current price of a bond can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the bond's par value at maturity). Given a 12% annual coupon rate on a $1,000 par value bond, the semiannual coupon payment is $60 ($1,000 * 12% / 2). With a market rate of 16% annually or 8% semiannually, and 15 years to maturity (or 30 semiannual periods), the bond's price is calculated as follows:$$ \text{Current Price} = \frac{C}{r} \left(1 - \frac{1}{(1 + r)^n}\right) + \frac{F}{(1 + r)^n} $$Where:- $C$ is the semiannual coupon payment ($60),- $r$ is the semiannual market rate (0.08),- $n$ is the total number of semiannual periods (30),- $F$ is the face value of the bond ($1,000).Plugging in the values:$$ \text{Current Price} = \frac{60}{0.08} \left(1 - \frac{1}{(1 + 0.08)^{30}}\right) + \frac{1000}{(1 + 0.08)^{30}} $$$$ \text{Current Price} \approx 774.84 $$Therefore, the current price of the bond is approximately $774.84.