Problem

The balance on a credit card, that charges a $12 \%$ APR interest rate, over a 1 month period is given in the following table:
\begin{tabular}{|lll|}
\hline Days 1-3: & $\$ 150$ & (initial balance) \\
Days 4-20: & $\$ 200$ & ( $\$ 50$ purchase) \\
Days 21-30: & $\$ 50$ & ( $\$ 150$ payment) \\
\hline
\end{tabular}

What is the finance charge, on the average daily balance, for this card over this 1 month period?
finance charge $=\$[?]$

Answer

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Answer

The finance charge for this card over this 1 month period is \(\boxed{1.45}\).

Steps

Step 1 :Calculate the total balance for each period: for days 1-3 it's \(150 \times 3 = 450\), for days 4-20 it's \(200 \times 17 = 3400\), and for days 21-30 it's \(50 \times 10 = 500\).

Step 2 :Add these balances together to get the total balance for the month: \(450 + 3400 + 500 = 4350\).

Step 3 :Divide the total balance by the number of days in the month to get the average daily balance: \(4350 \div 30 = 145.0\).

Step 4 :Calculate the monthly interest rate by dividing the annual rate by 12: \(12\% \div 12 = 1\%\).

Step 5 :Finally, calculate the finance charge by multiplying the average daily balance by the monthly rate: \(145.0 \times 1\% = 1.45\).

Step 6 :The finance charge for this card over this 1 month period is \(\boxed{1.45}\).

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