Question

What rate of interest compounded continuously will yield an effective interest rate of 6%?

Short answer

The rate of interest that when compounded continuously will yield an effective interest rate of 6% is 5.827%

Step-by-step solution

Step 1. Given Information

Given to determine the rate of interest that when compounded continuously will yield an effective interest rate of 6%

Step 2. Calculation

The effective rate of interest r_e for an investment with rate of interest r and compounded continuously is given by $r_e=e^r-1$

Here the effective rate of interest is 6%, the decimal form is given by $r_e=0.06$

Plugging the values:

$$\begin{gathered} r_e=e^r-1 \\ 0.06=e^r-1 \\ {e}^r=0.06+1 \\ {e}^r=1.06 \\ r=\ln \left(1.06\right) \\ r=0.058268 \end{gathered}$$

Step 3. Conclusion

The rate of interest that when compounded continuously will yield an effective interest rate of 6% is 5.827%