Question

The zero coupon bonds of Mark Enterprises have a market price of $394.47, a face value of $1,000, and a yield to maturity of 6.87 percent based on semiannual compounding. How many years is it until this bond matures?

Answer 1

The time until the bond matures can be calculated using the present value formula. By plugging in the given values, it will take approximately 15 years for the bond to mature.

Step-by-step explanation:

The time until the bond matures can be calculated using the formula for present value:

Present Value (PV) = Face Value / (1 + Yield to Maturity / 2)^(2 * Number of Years)

Rearranging the formula to solve for Number of Years:

Number of Years = log(Face Value / Present Value) / (2 * log(1 + Yield to Maturity / 2))

Plugging in the given values:

Present Value = $394.47

Face Value = $1,000

Yield to Maturity = 6.87%

Calculating the number of years:

1. Calculate log(Face Value / Present Value) / (2 * log(1 + Yield to Maturity / 2))
2. Divide the result by 2 to get the number of years

By following these steps, we find that it will take approximately 15 years for the bond to mature.