Final answer:
The price of a zero-coupon bond with a 9% yield and $5,000 par value can be calculated using the formula P = M / (1 + r)^n, considering the semi-annual interest of 4.5% (9%/2) and doubling the number of periods for each maturity due to semi-annual pay-out.
Step-by-step explanation:
The student's question relates to calculating the price of a zero-coupon bond issued by the Wosley Company with different maturities and a semi-annual convention. The bond yield is projected to be 9%, and the par value is $5,000.
The price of a zero-coupon bond can be calculated using the formula P = M / (1 + r)n, where P is the present value (price) of the bond, M is the par value at maturity, r is the yield per period, and n is the number of periods until maturity. Since it is a semi-annual convention, the yield per period (r) is 9%/2 = 4.5%, and the number of periods is double the number of years to maturity.
Therefore, for different maturities:
- For a 20-year maturity: n = 40 (20 years x 2 because of semi-annual)
- For a 40-year maturity: n = 80 (40 years x 2)
- For a 70-year maturity: n = 140 (70 years x 2)
- For a 90-year maturity: n = 180 (90 years x 2)
To obtain the exact bond prices, one would simply substitute the values of M, r, and n for each maturity into the formula mentioned above.