Betty deposits $5,000 now and deposits $3,000 after 1 year and deposits $2,000 after 2 years. 3 years after the initial deposit her account balance is $12,713.74. Bob deposits $8,000 now and withdraws $2,500 after 1 year and deposits $1,000 after 2 years. 3 years after his initial deposit his account balance is $8,895.17. Bertha deposits $6,000 now and withdraws $1,500 after 1 year and withdraws $3,000 after 2 years. 3 years after her initial deposit her account balance is $2,815.89. If the continuous rates per annum are for the first year, for the second year, and for the third year then algebraically, find these three unknown rates. Your final answers should be correct to 2 places after the decimal point.

Please provide an explanation for the formulas used, thanks