An investment pays 1000 in one year, 2000 at the end of the second year and 3000 at the end of the third year. An investor has purchased it to yield an annual effective rate i = 0.08. Using the first-order modified approximation, i) Estimate the new price if the interest rate increases to 0.082. ii) Compare this estimated price to the actual price of the investment at i = 0.082.