What is the rate payable monthly that is equivalent to 9% continuously compounded?

1. Identify the continuous compounding annual rate \( r_c = 0.09 \).

r_c = 0.09

2. Convert the continuous compounding rate to the monthly rate using the formula:

r_m = e^{r_c / 12} - 1

3. Substitute the given continuous compounding rate into the formula:

r_m = e^{0.09 / 12} - 1

4. Calculate the exponential term:

e^{0.09 / 12} \approx 1.00753156

5. Subtract 1 to get the monthly rate:

r_m = 1.00753156 - 1
r_m \approx 0.0075

So, the rate payable monthly that is equivalent to 9% continuously compounded is approximately 0.0075 , or 0.75%.