A 6 year annuity pays $1,000 at the end of each year.
a. Compute the price of the annuity at an effective annual interest rate of 2%.
b. Compute the modified duration at an effective annual interest rate of 2%.
c. Compute the (Macaulay) duration at an effective annual interest rate of 2%.
d. Compute the modified convexity at an effective annual interest rate of 2%.
e. Compute the Macaulay convexity at an effective annual interest rate of 2%.
f. Estimate the new price of the annuity if the interest rate changes to 1.9% using the first- order modified approximation.
g. Estimate the new price of the annuity if the interest rate changes to 1.9% using the first-order Macaulay approximation.