please help only have a little over an hour. will upvote. even just answer a few of the questions will help.

Problem 3 (5 points): Consider a 1-factor parallel yield shift model with a flat structure of forward rates y. Assume currently y=6%. Note: this problem is calculation-heavy. Using formulas from PowerPoint slides instead of re-deriving them will help you save a lot of time.

a) (1 point) Find price, DV01, Duration, and Convexity of a 10-year zero-coupon bond. Keep at least 4 decimal digits

b) (1 point) Find price, DV01, Dmod, and Convexity of a perpetuity that pays $8 years coupons every 6 months (i.e. has an annual coupon of $16 paid semiannually). Keep at least 4 decimal digits

c) (1 point) You have a portfolio with a current market value of $500,000, Duration=14, and Convexity =400. If you want to hedge your portfolio using only 10-year zero-coupon bonds, how many bonds will you need to sell?

d) (2 points) You have a portfolio with a current market value of $500,000, Duration=14, and Convexity =400. If you want to hedge your portfolio using both 10-year zero-coupon bonds and perpetuites that pay $8 years coupons every 6 months (i.e. has an annual coupon of $16 paid semiannually. How many of each security you will need to buy or sell? Note: this is an especially calculation-heavy question. It may be a good idea to write down the equations that will be used to solve for the number of each security but to find the numerical solution only after you complete all other questions