Problem 1 . Consider a 25-year bond with face and maturity value of $100, with a coupon rate of 8% per annum payable semiannually, and a yield to...

Problem 1. Consider a 25-year bond with face and maturity value of $100, with a coupon rate of 8% per annum payable semiannually, and a yield to maturity of 5% per annum compounded semiannually. In the following your answers should be correct to 2 places after the decimal point.

1. Algebraically find the price.
2. Algebraically find the dollar duration.
3. Algebraically find modified duration. Be sure to state your answer in years.
4. Algebraically find the Macaulay duration. Be sure to state your answer in years.

Algebraically find the equation of the tangent line to the price versus yield graph at the above stated (semiannual) yield. Be sure to state your answer in slope-intercept form