You have some savings in a bank which is earning a $3\mathrm{.}5\%$ rate of interest. You want to begin a retirement fund for yourself by investing in the stock market. You believe you will need $$375,000$ to retire at your target date, twenty$-$seven years from now. You know that a long$-$term investment in a stock fund has typically paid a $7\mathrm{.}5\%$ per year return and you can invest in this fund. How much must vou withdraw from your savings account and invest today in the stock fund to realize the $ $375,000$ twenty$-$seven years from now?

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