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
Answer
Explanation:
Step1: Convert annual rate to daily rate
The annual percentage rate (APR) is 39% or 0.39 in decimal form. Assuming a 365 - day year, the daily interest rate $r$ is $\frac{0.39}{365}$.
Step2: Calculate the interest (fees)
The simple - interest formula is $I = Prt$, where $P=$1200$ is the principal amount, $r=\frac{0.39}{365}$ is the daily interest rate, and $t = 18$ days is the time. [ \begin{align*} I&=1200\times\frac{0.39}{365}\times18\ &=\frac{1200\times0.39\times18}{365}\ &=\frac{1200\times7.02}{365}\ &=\frac{8424}{365}\ &\approx23.08 \end{align*} ] Rounding to the nearest dollar, $I\approx$23$.
Answer:
b. $$23$