On March 22, Lisa bought a government guaranteed short term investment that will mature on October 13 of the same year. How much did Lisa pay for the investment if she will receive a maturity amount of $\$ 46,250.00$ on October 13 . The investment is growing at $4.70 \%$ p.a. simple interest?
Provide your answer rounded to the nearest cent.

Step 1 ：Given that the maturity amount is \( \$ 46,250.00 \), the annual interest rate is \(4.70 \%\), and the investment period is from March 22 to October 13 of the same year.

Step 2 ：We first need to calculate the time the money is invested for in years. The time period from March 22 to October 13 is 205 days. To convert this into years, we divide by 365: \(\frac{205}{365} \approx 0.5616 \) years.

Step 3 ：We can then use the formula for simple interest to calculate the initial investment. The formula is rearranged to solve for the initial investment: \(P = \frac{Maturity Amount}{1 + RT}\), where R is the annual interest rate (in decimal form) and T is the time the money is invested for in years.

Step 4 ：Substituting the given values into the formula, we get: \(P = \frac{46250.0}{1 + 0.047 * 0.5616} \approx 45060.53\)

Step 5 ：Final Answer: Lisa paid approximately \(\boxed{45060.53}\) for the investment.