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Mary age 30 today contributes an amount X at the beginning of each month into a fund which earns a nominal rate of 12% convertible monthly. Starting age 65, she will use the entire account balance to purchase an annuity at a nominal rate of 8% compounded semiannually, which will provide 5,000 at the beginning of each month to her as her retirement income until the end of her life. Calculate X. Show your work.


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