Final answer:
The number of years until the bond matures can be found by using the bond valuation formula and solving for the total number of periods until maturity. Financial calculators or spreadsheet software are typically used for this calculation. The required inputs are the current price, coupon payment, yield to maturity, and face value of the bond.
Step-by-step explanation:
The question asks about the number of years until a bond with a current market price of $774.50 and a face value of $1,000 matures. The bond has a coupon interest rate of 6.2 percent, payments are made semiannually, and the yield to maturity is set at 8.46 percent. To find the time to maturity, we must use the bond valuation formula that equates the present value of the payments plus the present value of the face value to the current market price.
In general, the process involves setting up the equation with all known values and then solving for the time (number of periods) to maturity. While the solution to this problem was not calculated in this answer, this type of problem is typically addressed using financial calculators or spreadsheet software where you input the known variables (current price, coupon payment, yield to maturity, and face value) to solve for the unknown variable, which in this case is the number of years to maturity.
To be precise, the equation for valuing a bond is:
P = C * [1 - (1 + r)^-n] / r + F / (1 + r)^n
where P is the current price of the bond, C is the coupon payment, r is the yield to maturity per period, n is the total number of periods, and F is the face value of the bond. This equation can help determine the exact time to maturity that tallies with the current yield.