The Lo Sun Corporation offers a 6% bond with a current market price of €875.05.The yield to maturity is 7.34%.The face value is €1,000.Interest is paid semiannually.How many years is it until
This bond matures?

Question

Quizplus · Accepted Answer

The bond's yield to maturity (YTM) can be calculated using the formula for the present value of a bond, which takes into account the present value of the bond's interest payments and the present value of its face value at maturity. Given that the bond pays interest semiannually, the annual interest rate of 6% is divided by 2 to get a semiannual interest rate of 3%, or €30 (€1,000 * 3%). The YTM of 7.34% annually is also divided by 2 for semiannual calculations, resulting in 3.67%. The bond's price is less than its face value, indicating it is selling at a discount, which happens when the market interest rate (YTM) is higher than the bond's coupon rate. Using the formula for the present value of a bond:$$ P = \frac{C}{r} \left(1 - \frac{1}{(1+r)^n}\right) + \frac{F}{(1+r)^n} $$where $P$ is the price of the bond (€875.05), $C$ is the semiannual interest payment (€30), $r$ is the semiannual yield (0.0367), $F$ is the face value (€1,000), and $n$ is the total number of semiannual periods until maturity.Rearranging the formula to solve for $n$ and substituting the given values can be complex and typically requires a financial calculator or an iterative numerical method since $n$ appears in an exponent. However, knowing the correct answer allows us to verify it:For 16 years (or 32 semiannual periods), plugging the values into the formula or using a financial calculator with these inputs should confirm that the bond's current market price aligns with the given YTM, indicating that the bond will mature in 16 years. This is a simplified explanation; the exact calculation involves more detailed financial mathematics.

The Lo Sun Corporation Offers a 6% Bond with a Current