document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201558>Question 1201558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. (Round your answer to the nearest cent.)<BR>\n" );
document.write( "Balance:    	$300<BR>\n" );
document.write( "Rate:    	17%<BR>\n" );
document.write( "Payment:    	$50<BR>\n" );
document.write( "Method:    	Adjusted balance\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848019 by </B><A HREF=/tutors/aboutme.mpl?userid=asinus><B>asinus(45)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=asinus><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate the monthly finance charge for the credit card transaction using the adjusted balance method, we will follow these steps:\r<BR>\n" );
document.write( "\n" );
document.write( "### Step 1: Calculate the Adjusted Balance\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Initial Balance**: $300<BR>\n" );
document.write( "2. **Payment Made**: $50<BR>\n" );
document.write( "3. **Days Until Payment is Processed**: 10 days<BR>\n" );
document.write( "4. **Days in the Billing Cycle**: 30 days\r<BR>\n" );
document.write( "\n" );
document.write( "Since the payment takes 10 days to process, the adjusted balance for the first 10 days is the full balance of $300. After the payment is processed, the balance will be reduced to $250 for the remaining 20 days.\r<BR>\n" );
document.write( "\n" );
document.write( "### Step 2: Calculate the Weighted Average Balance\r<BR>\n" );
document.write( "\n" );
document.write( "The weighted average balance can be calculated as follows:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Weighted Average Balance} = \left( \text{Balance}_1 \times \text{Days}_1 + \text{Balance}_2 \times \text{Days}_2 \right) / \text{Total Days}<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "Where:<BR>\n" );
document.write( "- $ \text{Balance}_1 = 300 $ (for the first 10 days)<BR>\n" );
document.write( "- $ \text{Days}_1 = 10 $<BR>\n" );
document.write( "- $ \text{Balance}_2 = 250 $ (for the remaining 20 days)<BR>\n" );
document.write( "- $ \text{Days}_2 = 20 $\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting the values:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Weighted Average Balance} = \left( 300 \times 10 + 250 \times 20 \right) / 30<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "Calculating the numerator:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "300 \times 10 = 3000<BR>\n" );
document.write( "$$<BR>\n" );
document.write( "$$<BR>\n" );
document.write( "250 \times 20 = 5000<BR>\n" );
document.write( "$$<BR>\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Total} = 3000 + 5000 = 8000<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "Now, divide by the total number of days:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Weighted Average Balance} = \frac{8000}{30} \approx 266.67<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "### Step 3: Calculate the Monthly Finance Charge\r<BR>\n" );
document.write( "\n" );
document.write( "The monthly finance charge is calculated using the formula:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Finance Charge} = \text{Weighted Average Balance} \times \left( \frac{\text{Annual Interest Rate}}{12} \right)<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "Where:<BR>\n" );
document.write( "- Annual Interest Rate = 17% = 0.17\r<BR>\n" );
document.write( "\n" );
document.write( "Calculating the monthly interest rate:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Monthly Interest Rate} = \frac{0.17}{12} \approx 0.01416667<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "Now, substituting the values into the finance charge formula:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\text{Finance Charge} = 266.67 \times 0.01416667 \approx 3.78<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "### Final Result\r<BR>\n" );
document.write( "\n" );
document.write( "Rounding to the nearest cent, the monthly finance charge is:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "\boxed{3.78}<BR>\n" );
document.write( "$$ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );