at what monthly rate was a capital of R$25,005 invested which yielded R$15,000 in interest over 6 months and 15 days

To solve for the monthly rate, we can use the formula for simple interest, which is: I=P\cdot r\cdot t

where:

- \( I \) is the interest earned,

- \( P \) is the principal amount,

- \( r \) is the monthly interest rate,

- \( t \) is the time in months.

Given: I=15,000.00 P=25,005.00 t=6.5 (assuming 1 month equals 30 days)

1. Substitute \( I \), \( P \), and \( t \) into the simple interest formula:

15,000 = 25,005 \cdot r \cdot 6.5

2. Rearrange the equation to solve for \( r \):

r = \frac{15,000}{25,005 \cdot 6.5}

3. Perform the computation:

r=\frac{15,000}{162,532.5}\approx0.0922892

4. Convert the decimal to a percentage:

r=9.22892\%

Answer: \( r \) is approximately 9.22892%.