lauras credit card has an apr of 12.04%, and it computes finance charges using the daily - balance method…
lauras credit card has an apr of 12.04%, and it computes finance charges using the daily - balance method and a 30 - day billing cycle. on june 1st, laura had a balance of $606.40. she made exactly one transaction in june: a payment of $55.25. if lauras finance charge for june was $5.71, on which day did she make the payment?\na. june 8th\nb. june 12th\nc. june 15th\nd. june 20th\nplease select the best answer from the choices provided\no a\no b\no c\no d
Answer
Explanation:
Step1: Calculate the daily - periodic rate
The APR is 12.04%. 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 with the initial balance of $B_1 = 606.40$ be $x$ days, and the number of days with the balance of $B_2=606.40 - 55.25=551.15$ be $30 - x$ days.
The finance charge $FC$ is calculated using the formula $FC = r\times$ (average daily balance) $\times30$. The average daily balance $ADB=\frac{B_1x + B_2(30 - x)}{30}$. So $FC=r\times\frac{B_1x + B_2(30 - x)}{30}\times30=r(B_1x + B_2(30 - x))$.
Substitute $B_1 = 606.40$, $B_2 = 551.15$, $r=\frac{0.1204}{365}$, and $FC = 5.71$ into the equation: [ \begin{align*} 5.71&=\frac{0.1204}{365}(606.40x+551.15(30 - x))\ 5.71\times365&=0.1204(606.40x + 16534.5-551.15x)\ 2084.15&=0.1204(55.25x + 16534.5)\ 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