A zero-coupon bond with a face value of $1,000 is issued with an initial price of $400.50. The bond matures in 23 years. What is the implicit interest, in dollars, for the first year of the bond’s life? Use semiannual compounding. a) $9.40 b) $10.10 c)

The implicit interest for the first year of the bond's life can be calculated using the formula: Implicit Interest = Face Value x (1 + Annual Interest Rate)^n - Initial Price where n is the number of periods in one year, which is 2 for semiannual compounding. First, we need to calculate the annual interest rate. We can use the formula: Initial Price = Face Value / (1 + Annual Interest Rate/2)^46 where 46 is the total number of semiannual periods in 23 years. Solving for Annual Interest Rate, we get: Annual Interest Rate = ((Face Value / Initial Price)^(1/46) - 1) x 2 Plugging in the values, we have: Annual Interest Rate = ((1000 / 400.50)^(1/46) - 1) x 2 ? 0.0505 or 5.05% Now, we can calculate the implicit interest for the first year: Implicit Interest = 1000 x (1 + 0.0505/2) - 400.50 ? $48.55 However, we are only interested in the implicit interest for one semiannual period or one year. We can divide the above value by 2 to get: Implicit Interest = $48.55 / 2 = $24.28 Therefore, the answer is not one of the given options.