Your grandmother gives you 240 dollars for your birthday, which you invest in a mutual fund on January 1, 2002. On June 1, 2002, she gives you 770 dollars for your high school graduation, which you immediately deposit into your mutual fund. On January 1, 2003, you take out your calculator and find that your dollar weighted rate of return for the previous year was 5.7 percent. On April 1, 2003 your fund balance is 1600 dollars and you then deposit your grandmother's Easter gift of $X$ dollars. On January 1, 2004, your fund balance is 2800 dollars and you calculate that your time weighted rate of return for the previous year was 11.6 percent. What is $X$? (As usual, assume simple interest for the dollar weighted rate of return, and months of equal length.)
Answer = dollars.