patrick has a credit card with an apr of 15.40% and a billing cycle of 30 days. the following table shows…

patrick has a credit card with an apr of 15.40% and a billing cycle of 30 days. the following table shows patricks credit card transactions in the month of august.\n| date | amount ($) | transaction |\n| ---- | ---- | ---- |\n| 8/1 | 1,466.22 | beginning balance |\n| 8/6 | 28.48 | purchase |\n| 8/9 | 150.00 | payment |\n| 8/17 | 115.75 | payment |\n| 8/20 | 40.00 | purchase |\n| 8/22 | 31.76 | purchase |\nhow much greater will patricks august finance charge be if his credit card company computes finance charges using the previous balance method than if it computes finance charges using the adjusted balance method?\n a. $2.44\n b. $3.41\n c. $2.13\n d. $4.69

patrick has a credit card with an apr of 15.40% and a billing cycle of 30 days. the following table shows patricks credit card transactions in the month of august.\n| date | amount ($) | transaction |\n| ---- | ---- | ---- |\n| 8/1 | 1,466.22 | beginning balance |\n| 8/6 | 28.48 | purchase |\n| 8/9 | 150.00 | payment |\n| 8/17 | 115.75 | payment |\n| 8/20 | 40.00 | purchase |\n| 8/22 | 31.76 | purchase |\nhow much greater will patricks august finance charge be if his credit card company computes finance charges using the previous balance method than if it computes finance charges using the adjusted balance method?\n a. $2.44\n b. $3.41\n c. $2.13\n d. $4.69

Answer

Explanation:

Step1: Calculate daily - periodic rate

The APR is 15.40% or 0.154 in decimal form. The daily - periodic rate $r$ is calculated by dividing the APR by 365. So, $r=\frac{0.154}{365}$.

Step2: Calculate finance charge using previous - balance method

The previous balance is $1466.22$. The finance charge $FC_{prev}$ using the previous - balance method for a 30 - day billing cycle is $FC_{prev}=1466.22\times\frac{0.154}{365}\times30$. $FC_{prev}=1466.22\times0.0004229\times30\approx18.65$.

Step3: Calculate adjusted balance

The adjusted balance is calculated as follows: Beginning balance = $1466.22$ Purchases: $28.48 + 40.00+31.76=100.24$ Payments: $150.00 + 115.75 = 265.75$ Adjusted balance $AB=1466.22+100.24 - 265.75=1300.71$.

Step4: Calculate finance charge using adjusted - balance method

The finance charge $FC_{adj}$ using the adjusted - balance method for a 30 - day billing cycle is $FC_{adj}=1300.71\times\frac{0.154}{365}\times30$. $FC_{adj}=1300.71\times0.0004229\times30\approx16.21$.

Step5: Calculate the difference

The difference $\Delta FC=FC_{prev}-FC_{adj}$. $\Delta FC = 18.65 - 16.21=2.44$.

Answer:

a. $$2.44$