i need help woth this money & banking problem

I Duration reflects whether the future cash payments of an asset are relatively short-term (low duration) or long-term (high duration). A way to measure duration is given by the following formula: duration=- where CP, is the cash payment periods in the future, Tis the time to maturity of the asset, and is the interest rate at which one discounts the future cash payments Note that following formulas might be helpful a. (5 points) Assume that the interest rate is 10% (-0.1). Calculate the duration for a zero coupon bond that matures in ten years with a cash payment of $10,000 at the time the bond matures and no cash payments before the maturity date. Show work b. (5 points) Assume that the interest rate is 10% (-0.1). Calculate the duration for a bond that pays $1100 in one year, S1210 in two years, and 1331 in three years. What is the present value of this asset today? What is the duration of this asset? Show work c. (5 points) A mortgage interest payment is $20,000 per year for the next 30 years. Suppose the interest rate is 5%. What is the value of that mortgage today? What is the duration of that mortgage? Show work. d. (5 points) Suppose the yield to maturity of a consolisi-0.05. Calculate the duration a consol that pays $100 cach year. Hint: In the above formulas T-00 so that a' is going to zero faster than T is going to infinity. Show work. c. (5 points) Suppose the yield to maturity on the consol in part d increases to 10% What is the duration of that consol? Show work. Explain why has the duration on this consol has changed even though the maturity date if the consol remains the same