Joe has an amount of money X that he would like to invest in some way. He has two options: He can invest the money in an account that pays an annual effective rate of interest of 9%. Joe would receive an interest payment at the end of each year and reinvest it in another account that pays an annual effective rate of interest of 6%. This will continue for 15 years. Joe can lend the money to his friend Ted, who will repay Joe with a series of 15 yearly payments. Each payment will be $100, and the first payment will occur in one year. Joe will reinvest these payments at an annual effective rate of interest of 6%. Joe notices that the amount of money that he will have at the end of 15 years is the same under either option. To the nearest dollar, what is the amount of money X?
Joe has an amount of money X that he would like to invest in some way. He has two options: He can invest the money in an account that pays an annual effective rate of interest of 9%. Joe would receive an interest payment at the end of each year and reinvest it in another account that pays an annual effective rate of interest of 6%. This will continue for 15 years. Joe can lend the money to his friend Ted, who will repay Joe with a series of 15 yearly payments. Each payment will be $100, and the first payment will occur in one year. Joe will reinvest these payments at an annual effective rate of interest of 6%. Joe notices that the amount of money that he will have at the end of 15 years is the same under either option. To the nearest dollar, what is the amount of money X?
A $406.00
B $417.00
C $752.00
D $1,063.00
E $1,111.00
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