To pay for a home improvement project that totals $9,000, Genesis is choosing between taking out a simple interest bank loan at 9% for 3 years or paying with a credit card that compounds monthly at an annual rate of 18% for 7 years. Which plan would give Genesis the lowest monthly payment?

The monthly credit card payment would be $295, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $272.50, which is lower than the monthly credit card payment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
The monthly credit card payment would be $374.21, which is lower than the monthly payment on the bank loan.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ A=9000[1+(0.09)(3)] \implies \boxed{A = 11430}[/tex]

now, that's for 36 months, so she'd be owing the Bank per month [tex]\cfrac{\stackrel{total}{11430}}{\underset{months}{36}}~~ = ~~\text{\LARGE 317.5}[/tex]

now let's take a look at the Credit Card's loan at 18% for 7 years

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9000\\ r=rate\to 18\%\to \frac{18}{100}\dotfill &0.18\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases} \\\\\\ A=9000\left(1+\frac{0.18}{12}\right)^{12\cdot 7} \implies A \approx \boxed{31433.31}[/tex]

now, in 7 years there are 84 months, thus [tex]\cfrac{\stackrel{total}{31433.31}}{\underset{months}{84}}\approx \text{\LARGE 374.21}[/tex]

so, the Bank will give her a better deal per month, and to be honest altogether.