the following table shows the balance on a cr...
the following table shows the balance on a credit card over the period of 1 month, that charges a 20% apr (interest rate).\ndays balance description\n1 - 3 $150 initial balance\n4 - 20 $200 $50 purchase\n21 - 30 $50 $150 payment\nwhat is the finance charge, on the average daily balance, for this card over this 1 month period?\nfinance charge = $?\nround to the nearest cent
Answer
# Explanation:
## Step1: Calculate weighted - balance for each period
For days 1 - 3: The balance is $150$ for $3$ days. The weighted - balance is $150\times3 = 450$.
For days 4 - 20: The balance is $200$ for $17$ days. The weighted - balance is $200\times17=3400$.
For days 21 - 30: The balance is $50$ for $10$ days. The weighted - balance is $50\times10 = 500$.
## Step2: Calculate the average daily balance
The total number of days is $3 + 17+10=30$ days.
The sum of weighted - balances is $450 + 3400+500=4350$.
The average daily balance (ADB) is $\frac{4350}{30}=145$.
## Step3: Calculate the monthly interest rate
The annual percentage rate (APR) is $20\%=0.2$. The monthly interest rate $r$ is $\frac{0.2}{12}$.
## Step4: Calculate the finance charge
The finance charge $FC$ is $FC = ADB\times r$.
$FC=145\times\frac{0.2}{12}\approx2.42$.
# Answer:
$2.42$