Allison and Leslie, who are twins, just received $$45,000$ each for their $29$th birthday. They both have aspirations to become millionaires. Each plans to make a $$5,000$ annual contribution to her "early retirement fund" on her birthday, beginning a year from today. Allison opened an account with the Safety First Bond Fund, a mutual fund that invests in high$-$quality bonds whose investors have earned $5\%$ per year in the past. Leslie invested in the New Issue Bio$-$Tech Fund, which invests in small, newly issued bio$-$tech stocks and whose investors have earned an average of $16\%$ per year in the fund's relatively short history.

How large would Allison's annual contributions have to be for her to become a millionaire at the same age as Leslie, assuming their expected returns are realized? Do not round intermediate calculations. Round your answer to the nearest cent.

Please explain how this would be solved with a financial calculator.