Suppose there is a 5-year bond with $5,000 par value that pays a 5% coupon with interest rates currently at 5%.

1) What is the duration of the bond?

2) What is the convexity of the bond?

3) Suppose the interest rate rises to 6% but the coupon rate stays the same at 5%, answer (a-c for question 3 only)

a. What is the new bond price using the duration approximation (without using convexity)?

b. What is the new bond price using the duration and convexity approximation?

c. What is the new bond price when discounting the cash flows at this new rate?

Please show calculations for all work, thanks!