Chapter 4 - Exponential Functions - 4.4 Applications to Compound Interest - Exercises and Problems for Section 4.4 - Exercises and Problems - Page 167: 5

$8.3 \%$ per year

Let $P$ be the initial amount, the amount after 8 years is $0.5 P$. To find the effective annual yield, we set $P b^8$ equal to $0.5 P$ and solve for $b$ : $$ \begin{aligned} b^8 & =0.5 \\ b & =(0.5)^{1 / 8}=0.917 \end{aligned} $$ Therefore, the effective interest rate by which the investment has decreased is $$i= 1-0.917=8.3\%$$