Jane just turns 30 years old and wants to start a savings plan, where she contributes $X every month to a savings account, starting one month from now until she reaches 65 years old. From her 65th birthday, she wishes to withdraw $1500 per month for 12 months at the beginning of each month, with the first withdrawal happening on the 65th birthday. Over the next 20 years, her monthly withdrawal will increase by 3% in comparison to previous year (i.e., withdraw $1500 x 1.03 per month in the 2nd year, $1500 x 1.032 per month in the 3rd year, etc). Her last withdrawal will occur 1 month before her 85th birthday. Given that the savings account has 12% annual nominal interest rate, compounded monthly, what is X?
Jane just turns 30 years old and wants to start a savings plan, where she contributes $X every month to a savings account, starting one month from now until she reaches 65 years old. From her 65th birthday, she wishes to withdraw $1500 per month for 12 months at the beginning of each month, with the first withdrawal happening on the 65th birthday. Over the next 20 years, her monthly withdrawal will increase by 3% in comparison to previous year (i.e., withdraw $1500 x 1.03 per month in the 2nd year, $1500 x 1.032 per month in the 3rd year, etc). Her last withdrawal will occur 1 month before her 85th birthday. Given that the savings account has 12% annual nominal interest rate, compounded monthly, what is X?
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