freidas credit card has an apr of 13.73%, and it calculates her finance charge by using the daily balance…

freidas credit card has an apr of 13.73%, and it calculates her finance charge by using the daily balance method and a 30 - day billing cycle. on september 1st, freida had a balance of $449.22. during the month of september, she made a payment of $85.33 and a purchase of $60.99. how much greater will her september finance charge be if the purchase occurred on september 7th and the payment occurred on september 20th than it would be if the payment occurred on september 7th and the purchase occurred on september 20th?\na. $0.13\nb. $0.41\nc. $0.72\nd. $0.28

freidas credit card has an apr of 13.73%, and it calculates her finance charge by using the daily balance method and a 30 - day billing cycle. on september 1st, freida had a balance of $449.22. during the month of september, she made a payment of $85.33 and a purchase of $60.99. how much greater will her september finance charge be if the purchase occurred on september 7th and the payment occurred on september 20th than it would be if the payment occurred on september 7th and the purchase occurred on september 20th?\na. $0.13\nb. $0.41\nc. $0.72\nd. $0.28

Answer

Explanation:

Step1: Calculate daily - interest rate

The APR is 13.73%, so the daily - interest rate $r=\frac{0.1373}{365}$.

Step2: Case 1: Purchase on Sep 7th and payment on Sep 20th

The balance for the first 6 days is $B_1 = 449.22$. The balance from day 7 to day 19 is $B_2=449.22 + 60.99=510.21$. The balance from day 20 to day 30 is $B_3=510.21-85.33 = 424.88$. The average daily balance $ADB_1=\frac{449.22\times6 + 510.21\times13+424.88\times11}{30}$ [ \begin{align*} ADB_1&=\frac{2695.32+6632.73 + 4673.68}{30}\ &=\frac{13991.73}{30}\ & = 466.391 \end{align*} ] The finance charge $FC_1=ADB_1\times r\times30=466.391\times\frac{0.1373}{365}\times30$.

Step3: Case 2: Payment on Sep 7th and purchase on Sep 20th

The balance for the first 6 days is $B_4 = 449.22$. The balance from day 7 to day 19 is $B_5=449.22-85.33 = 363.89$. The balance from day 20 to day 30 is $B_6=363.89+60.99 = 424.88$. The average daily balance $ADB_2=\frac{449.22\times6+363.89\times13 + 424.88\times11}{30}$ [ \begin{align*} ADB_2&=\frac{2695.32+4730.57+4673.68}{30}\ &=\frac{12099.57}{30}\ &=403.319 \end{align*} ] The finance charge $FC_2=ADB_2\times r\times30=403.319\times\frac{0.1373}{365}\times30$.

Step4: Calculate the difference

The difference $\Delta FC=(FC_1 - FC_2)$ [ \begin{align*} \Delta FC&=(466.391 - 403.319)\times\frac{0.1373}{365}\times30\ &=63.072\times\frac{0.1373}{365}\times30\ &\approx0.72 \end{align*} ]

Answer:

c. $0.72$