Final answer:
The corporation will have to pay approximately $9,995,420.23 to retire the debt on the maturity date.
Step-by-step explanation:
To find out how much the corporation will have to pay to retire the debt on the maturity date, we need to calculate the present value of the bond's future cash flows. The bond pays 6% annual interest semiannually, so it pays 3% interest every six months. The bond has a par (face) value of $10,000,000, and it was issued for $9,600,000. Since the interest payments are semiannual, there will be 20 interest payments over the 10-year period.
To calculate the present value, we use the formula:
PV = C × ((1 - (1 + r)^(-n)) / r) + F / (1 + r)^n
Where:
- PV is the present value
- C is the periodic interest payment
- r is the periodic interest rate
- n is the number of periods
- F is the face value of the bond
Using the given information, we can calculate the present value:
Periodic interest payment = 0.03×$10,000,000 = $300,000
Periodic interest rate = 0.03
Number of periods = 20
Face value of the bond = $10,000,000
Using the formula, PV = $300,000 × ((1 - (1 + 0.03)^(-20)) / 0.03) + $10,000,000 / (1 + 0.03)^20
The corporation will have to pay approximately $9,995,420.23 to retire the debt on the maturity date.