On April $10,$ Brooke bought a government guaranteed short term investment that will mature on November $15$ of the same year. How much did Brooke pay for the investment if she will receive a maturity amount of $$49,000\mathrm{.}00$ on November $15.$ The investment is growing at $5\mathrm{.}10\%$ p$.$a$.$ simple interest?

Provide your answer rounded to the nearest cent.