Final answer:
The highest price an investor can pay for the bond and obtain an annual effective yield of at least 10% is $1,104.83.
Step-by-step explanation:
The highest price (x) that an investor can pay for the bond and obtain an annual effective yield of at least 10% can be calculated using the following steps:
Using the given information, the coupon rate is 10% and the annual effective interest rate is 10%. Thus, the semi-annual effective interest rate is 5%. The bond has 30 semi-annual coupon payments of $50 each and a par value of $1,000. To calculate the present value of the coupons, we can use the formula:
PV = C((1 - (1 + r)^(-n))/(r))
Where PV is the present value of the coupons, C is the coupon payment, r is the semi-annual effective interest rate, and n is the number of semi-annual coupon payments. Plugging in the values, we get:
PV = 50((1 - (1 + 0.05)^(-30))/(0.05)) = $746.87
Next, to calculate the present value of the par value, we can use the formula:
PV = F(1 + r)^(-n)
Where PV is the present value of the par value, F is the par value, r is the semi-annual effective interest rate, and n is the number of semi-annual periods until maturity. Plugging in the values, we get:
PV = 1000(1 + 0.05)^(-60) = $357.96
Finally, we can sum the present values of the coupons and par value to calculate the maximum price (x) that the investor can pay:
x = PV of coupons + PV of par value = 746.87 + 357.96 = $1,104.83
Therefore, the highest price an investor can pay for the bond and obtain an annual effective yield of at least 10% is $1,104.83.