Twins graduate from college together at age 21 and start their careers. Twin 1 invests $2000 at the end of each of 15 years in an account that earns 10 % compounded annually. After the initial 15 years, no additional contributions are made, but the investment continues to earn 10 % compounded annually. Twin 2 invests no money for 15 years but then contributes a fixed amount at the end of each year until she is 65 years old to an account that pays 10 % compounded annually.

a) How much does Twin #1 have in her account at age 65? $

b) How much should Twin #2 deposit at the end of each year until age 65 so that she will have the same amount as Twin #1? $

c) Find the total amount Twin #1 deposited. $

d) Find the total amount Twin #2 deposited.