michael has a credit card with an apr of 15.33%. it computes finance charges using the daily balance method…

Explanation:

Step1: Calculate the daily - periodic rate

The APR is 15.33% or 0.1533 in decimal form. The daily - periodic rate $r$ is calculated by dividing the APR by 365. So, $r=\frac{0.1533}{365}$.

Step2: Let the number of days with the initial balance of $822.05$ be $x$ days. Then the number of days with the balance of $822.05 + 77.19=899.24$ is $(30 - x)$ days.

The finance charge formula for the daily - balance method is $FC = AD \times r\times30$, where $AD$ is the average daily balance. The average daily balance $AD=\frac{822.05x + 899.24(30 - x)}{30}$. And we know that $FC = 10.71$.

Step3: Substitute the values into the finance - charge formula

$10.71=\left(\frac{822.05x + 899.24(30 - x)}{30}\right)\times\frac{0.1533}{365}\times30$ First, simplify the right - hand side of the equation: $10.71=\frac{822.05x+899.24\times30 - 899.24x}{30}\times\frac{0.1533}{365}\times30$ $10.71=\frac{(822.05x - 899.24x)+26977.2}{30}\times\frac{0.1533}{365}\times30$ $10.71=\frac{- 77.19x + 26977.2}{30}\times\frac{0.1533}{365}\times30$ $10.71=\frac{(-77.19x + 26977.2)\times0.1533}{365}$ $10.71\times365=(-77.19x + 26977.2)\times0.1533$ $3909.15=(-77.19x + 26977.2)\times0.1533$ $\frac{3909.15}{0.1533}=-77.19x + 26977.2$ $25500=-77.19x + 26977.2$ $77.19x=26977.2 - 25500$ $77.19x = 1477.2$ $x = 19$

Step4: Determine the day of the purchase

Since $x = 19$, the purchase was made on the 20th day of April.

Answer:

d. April 20th