lauras credit card has an apr of 12.04%, and it computes finance charges using the daily balance method and…

Explanation:

Step1: Calculate the daily - periodic rate

The APR is 12.04% or 0.1204 in decimal form. The daily - periodic rate $r$ is calculated by dividing the APR by 365. So, $r=\frac{0.1204}{365}$.

Step2: Let the number of days before the payment be $x$.

The balance before the payment is $B_1 = 606.40$ and the balance after the payment is $B_2=606.40 - 55.25=551.15$. The finance charge is calculated as the sum of the interest on the first - part balance and the interest on the second - part balance. The interest on the first - part balance for $x$ days is $I_1=B_1\times r\times x$, and the interest on the second - part balance for $(30 - x)$ days is $I_2=B_2\times r\times(30 - x)$. The total finance charge $I = I_1+I_2$. We know that $I = 5.71$, $B_1 = 606.40$, $B_2 = 551.15$, and $r=\frac{0.1204}{365}$. Substitute the values into the equation: [ \begin{align*} 5.71&=606.40\times\frac{0.1204}{365}\times x+551.15\times\frac{0.1204}{365}\times(30 - x)\ 5.71&=\frac{0.1204}{365}(606.40x + 551.15\times30-551.15x)\ 5.71&=\frac{0.1204}{365}(55.25x+16534.5)\ 5.71\times365&=0.1204(55.25x + 16534.5)\ 2084.15&=0.1204\times55.25x+0.1204\times16534.5\ 2084.15&=6.6521x + 1980.7538\ 6.6521x&=2084.15 - 1980.7538\ 6.6521x&=103.3962\ x&=\frac{103.3962}{6.6521}\ x& = 15.54\approx15 \end{align*} ]

Answer:

c. June 15th