A $\$ 2800$ certificate of deposit held for 53 days was worth $\$ 2835.86$. What simple interest rate was earned? Assume a 360 -day year.
The certificate of deposit earned an interest rate of $\%$. (Type an integer or decimal rounded to the nearest tenth as needed.)

Step 1 ：Given that the initial investment (P) is $2800, the final amount (P + I) is $2835.86, and the time (T) is 53/360 years.

Step 2 ：We can find the interest earned (I) by subtracting the initial investment from the final amount: \(I = 2835.86 - 2800 = 35.86\)

Step 3 ：We then use the formula for simple interest, \(I = PRT\), to solve for the annual interest rate (R): \(R = \frac{I}{PT} = \frac{35.86}{2800 \times 0.147} = 0.087\)

Step 4 ：The result R is the annual interest rate in decimal form. To convert it to a percentage, we need to multiply it by 100: \(R_{\%} = 0.087 \times 100 = 8.7\%\)

Step 5 ：Final Answer: The certificate of deposit earned an interest rate of \(\boxed{8.7\%}\)