Chapter 4 - Exponential Functions - 4.4 Applications to Compound Interest - Exercises and Problems for Section 4.4 - Exercises and Problems - Page 167: 20

a) $ 7.763 \% $ b) $ 7.5 \% $

a) Given $M=M_0(1.07763)^t$ The effective annual rate is given by $$ \begin{aligned} i& =b-1 \\ & = 1.07763-1\\ & = 0.07763 =7.763\%\\ \end{aligned} $$ b) Since interest is compounded monthly, the nominal interest rate is $$ \begin{aligned} \left(1+\frac{r}{12}\right)^{12}& = 1.07763\\ r& = (12)1.07763^{1/12}-12=7.5\% \end{aligned} $$