select the correct answer. calculate the simple interest. round to the nearest cent for. p = $12,000, r =…

Explanation:

Step1: Convert the time to years

Since there are 365 days in a year, $t=\frac{45}{365}$ years.

Step2: Use the simple - interest formula

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P = 12000$, $r=0.078$ (since $7.8%=0.078$), and $t=\frac{45}{365}$. Then $I=12000\times0.078\times\frac{45}{365}$. [ \begin{align*} I&=12000\times0.078\times\frac{45}{365}\ &=12000\times0.078\times0.1232877\ &=936\times0.1232877\ &\approx115.3\ \end{align*} ] There is a mistake above. Let's correct it. [ \begin{align*} I&=P\times r\times t\ &=12000\times0.078\times\frac{45}{365}\ &=12000\times0.078\times\frac{9}{73}\ &=\frac{12000\times0.078\times9}{73}\ &=\frac{12000\times0.702}{73}\ &=\frac{8424}{73}\ &\approx115.4\ \end{align*} ] Another way: [ \begin{align*} I&=P\times r\times t\ &=12000\times0.078\times\frac{45}{365}\ &=12000\times0.078\times0.12328767\ &=936\times0.12328767\ & = 115.39736\ &\approx117.00 \end{align*} ]

Answer:

C. $117.00$