antonios credit card has an apr of 16.65%, and it calculates his finance charge by using the daily balance…

antonios credit card has an apr of 16.65%, and it calculates his finance charge by using the daily balance method and a 30 - day billing cycle. on june 1st, antonio had a balance of $811.67. during the month of june, he made a payment of $110.16 and a purchase of $84.04. how much greater will his june finance charge be if the purchase occurred on june 5th and the payment occurred on june 23rd than it would be if the payment occurred on june 5th and the purchase occurred on june 23rd? a. $0.44 b. $1.59 c. $4.96 d. $0.36

antonios credit card has an apr of 16.65%, and it calculates his finance charge by using the daily balance method and a 30 - day billing cycle. on june 1st, antonio had a balance of $811.67. during the month of june, he made a payment of $110.16 and a purchase of $84.04. how much greater will his june finance charge be if the purchase occurred on june 5th and the payment occurred on june 23rd than it would be if the payment occurred on june 5th and the purchase occurred on june 23rd? a. $0.44 b. $1.59 c. $4.96 d. $0.36

Answer

Explanation:

Step1: Calculate the daily - periodic rate

The APR is 16.65%. The daily - periodic rate $r$ is calculated by dividing the APR by 365. So $r=\frac{0.1665}{365}$.

Step2: Case 1: Purchase on June 5th and payment on June 23rd

  • The balance from June 1st - June 4th is $B_1 = 811.67$ for 4 days.
  • The balance from June 5th - June 22nd is $B_2=811.67 + 84.04=895.71$ for 18 days.
  • The balance from June 23rd - June 30th is $B_3=895.71-110.16 = 785.55$ for 8 days.
  • The average daily balance $ADB_1$ is $\frac{4\times811.67+18\times895.71 + 8\times785.55}{30}=\frac{3246.68+16122.78+6284.4}{30}=\frac{25653.86}{30}\approx855.13$.
  • The finance charge $FC_1=ADB_1\times r\times30=855.13\times\frac{0.1665}{365}\times30$.

Step3: Case 2: Payment on June 5th and purchase on June 23rd

  • The balance from June 1st - June 4th is $B_4 = 811.67$ for 4 days.
  • The balance from June 5th - June 22nd is $B_5=811.67-110.16 = 701.51$ for 18 days.
  • The balance from June 23rd - June 30th is $B_6=701.51 + 84.04=785.55$ for 8 days.
  • The average daily balance $ADB_2$ is $\frac{4\times811.67+18\times701.51+8\times785.55}{30}=\frac{3246.68 + 12627.18+6284.4}{30}=\frac{22158.26}{30}\approx738.61$.
  • The finance charge $FC_2=ADB_2\times r\times30=738.61\times\frac{0.1665}{365}\times30$.

Step4: Calculate the difference in finance charges

The difference $\Delta FC=FC_1 - FC_2=(855.13 - 738.61)\times\frac{0.1665}{365}\times30$ [ \begin{align*} \Delta FC&=(855.13 - 738.61)\times\frac{0.1665}{365}\times30\ &=116.52\times\frac{0.1665}{365}\times30\ &=116.52\times0.000456164\times30\ &=116.52\times0.01368492\ &\approx1.59 \end{align*} ]

Answer:

b. $$1.59$