Bob places $2,000 a year in his IRA for ten years and then invests $3,000 a year for the next ten years. Mary places $3,000 a year in her IRA for ten years and then invests $2,000 a year for the next ten years. They both have invested $50,000. If they earn 9 percent annually, how much more will Mary have earned than Bob at the end of 20 years? Round your answer to the nearest dollar.

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Bob places $2,000 a year in his IRA for ten years and then invests $3,000 a year for the next ten years. Mary places $3,000 a year in her IRA for ten years and then invests $2,000 a year for the next ten years. They both have invested $50,000. If they earn 9 percent annually, how much more will Mary have earned than Bob at the end of 20 years? Round your answer to the nearest dollar.

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hi for Bob he has 3 kinds of investments : 1- 2,000 $ a year for 10 years = 2,000 * (((1+0.09)^ 10 )- 1 ) / 0.09 = 2,000 * 15.192 = 30,384 $ 2- 30,384 $ constant with 9% in year for second 10 years = 30,384 * (1+ 0.09) ^ 10 = 30,384 * 2.367 = 71,919 $ 3- 3,000 $ a year just for second 10 years ! 3,000 * (((1+0.09)^20)- 1) / 0.09 - 3,000 * (((1+0.09)^10) - 1 ) / 0.09 **** it means that 20 years minus first 10 years **** 3,000 * 51.160 - 3,000 * 15.192 = 153,480 - 45,576 = 107, 913 $ ------------------------------------------ total = 71,919 + 107,913 = 179,832 $ and all of above calculates for Mary : ((3000 * 15.192) * 2.367 ) + (2000 * 51.160) - (2000 * 15.192) = ------------------------------------------ total = 107,878 + 71,936 = 179,814 $
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