lenny wants to save money to buy a motorcycle. She Invests in an ordinary annuity that earns $7.2 \%$ interest, compounded monthly. Payments will be made at the end of each month. How much money will she need to pay Into the annuity each month for the annulty to have a total value of $\$ 5000$ after 6 years? Do not round Intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. 5] Explanation Check

Step 1 ：We are given that Lenny wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 7.2% interest, compounded monthly. Payments will be made at the end of each month. We need to find out how much money she will need to pay into the annuity each month for the annuity to have a total value of $5000 after 6 years.

Step 2 ：To solve this problem, we need to use the formula for the future value of an ordinary annuity. The formula is: \(FV = P \times \left[(1 + \frac{r}{n})^{nt} - 1\right] / \frac{r}{n}\)

Step 3 ：In this formula, FV is the future value of the annuity, which is $5000 in this case. P is the payment made each period, which is what we're trying to find. r is the annual interest rate, which is 7.2% or 0.072. n is the number of times interest is compounded per year, which is 12 since it's compounded monthly. t is the number of years, which is 6.

Step 4 ：We can rearrange the formula to solve for P: \(P = FV \times \frac{r}{n} / \left[(1 + \frac{r}{n})^{nt} - 1\right]\)

Step 5 ：Now we can plug in the values and calculate P. FV = 5000, r = 0.072, n = 12, t = 6. After calculation, we get P = 55.72602839679716

Step 6 ：Rounding to the nearest cent, we get P = 55.73

Step 7 ：Final Answer: Lenny will need to pay approximately \(\boxed{55.73}\) into the annuity each month for the annuity to have a total value of $5000 after 6 years.