a company offering tax refund anticipation loans is trying to draw new customers. the company guarantees…
a company offering tax refund anticipation loans is trying to draw new customers. the company guarantees that the annual percentage rate on its loans is 39%. what fees would the company charge on a $1,200 loan if the term of the loan is 18 days? (round to the nearest dollar).\na. $18\nb. $23\nc. $28\nd. $30\nplease select the best answer from the choices provided.
Answer
Answer:
B. $23
Explanation:
Step1: Convert annual rate to daily rate
The annual percentage rate (APR) is 39% or 0.39 in decimal form. To find the daily interest rate $r_d$, we divide the annual rate by 365 days. So $r_d=\frac{0.39}{365}$.
Step2: Calculate the interest for 18 - day loan
The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the interest rate, and $t$ is the time. Here, $P=$1200$, $r = r_d=\frac{0.39}{365}$, and $t = 18$ days. [ \begin{align*} I&=1200\times\frac{0.39}{365}\times18\ &=1200\times0.39\times\frac{18}{365}\ & = 468\times\frac{18}{365}\ &=\frac{8424}{365}\ &\approx23.08 \end{align*} ] Rounding to the nearest dollar, the interest (fees) is $$23$.