## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$5.827 \%$
Effective Rate of Interest Formula for Continuous Compounding $$r_e = e^r-1$$ $r_e:$ Effective Rate of Interest $r:$ Annual Interest Rate $r_e = 0.06$ $0.06 = e^r -1$ $0.06+1 = e^r$ $1.06 = e^r$ Taking the natual logarithm of both sides $\ln{1.06} = \ln{e^r}$ $\ln{1.06} = r \ln{e}$ $\because \ln{e} = 1$ $\therefore \ln{1.06} = r$ $r \approx 0.05827$ $r = \boxed{5.827 \% }$
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