Chapter 3.4, Problem 65E

In Problems solver $65\text{-}68$, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places.

A discount electronics store offers to let you pay for a $\text{\$1,000}$ stereo in $12$ equal $\text{\$90}$ installments. The store claims that since you repay $\text{\$1,080}$ in $1$ year, the $\$80$ finance charge represents an $8\%$ annual rate. This would be true if you repaid the loan in a single payment at the end of the year. But since you start repayment after $1$ month, this is an amortized loan, and $8\%$ is not the correct rate. What is the annual nominal compounding rate for this loan?