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Sarah started working as an investment banker with a starting annual salary of $84,000 on January 1, 2014. She receives her salary in equal monthly instalments at the end of each month. She expects to receive a 4% raise every year until she retires after 30 years of hard work (i.e. she will receive monthly paycheques of $7,000 at the end of each month in 2014, $7,000 × 1.04 at the end of every month in 2015, and so on). As part of her benefits package her employer offers to put in 5% of her monthly paycheque into a retirement savings account as long as she puts in an equal amount at the same time (so if she puts $350 = 0.05 × $7,000 into the retirement account form her own salary at the end of this month, her employer will match that amount by an additional $350 so in total, $700 will be deposited into her retirement account on January 31, 2014). Assuming she will continue to contribute exactly 5% every month for 30 years, how much money will Sarah have in her retirement account by the time she retires? (Her last work day and paycheque will fall on December 31st, so assume she and her employer make one last payment into the account and then she checks her balance.) Sarah earns 6.6% (APR, compounded monthly) interest on funds invested in her retirement account.
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