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\nplease select the best answer from the choices provided

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\nplease select the best answer from the choices provided

Answer

Answer:

A. $0.13

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 7th, payment on 20th

The balance for the first 6 days is $B_1 = 449.22$. The balance from 7th to 19th (13 days) is $B_2=449.22 + 60.99=510.21$. The balance from 20th to 30th (11 days) is $B_3=510.21 - 85.33 = 424.88$. The average daily balance $ADB_1=\frac{449.22\times6 + 510.21\times13+424.88\times11}{30}$ $ADB_1=\frac{2695.32+6632.73 + 4673.68}{30}=\frac{13991.73}{30}=466.391$ The finance charge $FC_1=ADB_1\times r\times30=466.391\times\frac{0.1373}{365}\times30$

Step3: Case 2: Payment on 7th, purchase on 20th

The balance for the first 6 days is $B_4 = 449.22$. The balance from 7th to 19th (13 days) is $B_5=449.22-85.33 = 363.89$. The balance from 20th to 30th (11 days) is $B_6=363.89 + 60.99=424.88$. The average daily balance $ADB_2=\frac{449.22\times6+363.89\times13 + 424.88\times11}{30}$ $ADB_2=\frac{2695.32+4730.57+4673.68}{30}=\frac{12099.57}{30}=403.319$ The finance charge $FC_2=ADB_2\times r\times30=403.319\times\frac{0.1373}{365}\times30$

Step4: Calculate the difference

$\Delta FC=FC_1 - FC_2=(ADB_1 - ADB_2)\times\frac{0.1373}{365}\times30$ $(466.391 - 403.319)\times\frac{0.1373}{365}\times30=63.072\times\frac{0.1373}{365}\times30\approx0.13$