use the average daily balance method to compute the finance charge on the credit - card account for the…

use the average daily balance method to compute the finance charge on the credit - card account for the month of august (31 days). the starting balance from the previous month is $230. the transactions on the account for the month are given in the table to the right. assume an annual interest rate of 21% on the account and that the billing date is august 1st.\nthe finance charge for the month of august is $ \n(round to the nearest cent as needed.)\n| date | transaction |\n| ---- | ---- |\n| august 8 | made payment of $75 |\n| august 9 | charged $150 for hiking boots |\n| august 19 | charged $24 for gasoline |\n| august 27 | charged $32 for restaurant meal |

use the average daily balance method to compute the finance charge on the credit - card account for the month of august (31 days). the starting balance from the previous month is $230. the transactions on the account for the month are given in the table to the right. assume an annual interest rate of 21% on the account and that the billing date is august 1st.\nthe finance charge for the month of august is $ \n(round to the nearest cent as needed.)\n| date | transaction |\n| ---- | ---- |\n| august 8 | made payment of $75 |\n| august 9 | charged $150 for hiking boots |\n| august 19 | charged $24 for gasoline |\n| august 27 | charged $32 for restaurant meal |

Answer

Explanation:

Step1: Calculate balance after each transaction

  • Starting balance (August 1 - August 7): $230$ for $7$ days.
  • After payment on August 8: $230 - 75=155$. Balance from August 8 - August 8: $155$ for $1$ day.
  • After charge on August 9: $155 + 150 = 305$. Balance from August 9 - August 18: $305$ for $10$ days.
  • After charge on August 19: $305+24 = 329$. Balance from August 19 - August 26: $329$ for $8$ days.
  • After charge on August 27: $329+32 = 361$. Balance from August 27 - August 31: $361$ for $5$ days.

Step2: Calculate sum of (balance * number of days)

[230\times7+155\times1 + 305\times10+329\times8+361\times5] [=1610+155 + 3050+2632+1805] [=9252]

Step3: Calculate average daily balance

Average daily balance $=\frac{9252}{31}\approx298.45$

Step4: Calculate monthly interest rate

Annual interest rate is $21%=0.21$. Monthly interest rate $r=\frac{0.21}{12}=0.0175$

Step5: Calculate finance charge

Finance charge $=298.45\times0.0175\approx5.22$

Answer:

$5.22$