Determine the annual interest rate r required for an investment with continuous compound interest to yield an effective rate of 9.94%.

To determine the annual interest rate required for an investment with continuous compound interest, we can use the formula for the effective rate:

A = P * e^(rt)

Where:
A = Final amount
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate
t = Time in years

In this case, we want to find the annual interest rate (r), so we rearrange the formula and solve for 'r':

r = (ln(A/P))/t

Given that the effective rate is 9.94% and assuming the initial investment (P) is 1, the final amount (A) would also be 1.0994 (since it represents 1 unit plus 9.94% interest).

r = (ln(1.0994/1))/t

The time (t) in this case is not provided, so we cannot calculate the exact annual interest rate. However, we can still demonstrate the steps on how to find it, assuming a 1-year investment period.

r = (ln(1.0994))/1

Using a calculator or software that has a natural logarithm function, we can find the value of ln(1.0994), which is approximately 0.0956.

Therefore, assuming a 1-year investment period, the annual interest rate (r) required for an investment with continuous compound interest to yield an effective rate of 9.94% is approximately 0.0956, or 9.56%.