document.write( "Question 1171661: You have a balance of $2600 on your Visa credit card. Assume that you make no more charges on the card and that the card charges 9.6% APR and requires a minimum payment of 3% of the balance. Assume also that you make only the minimum payments.\r
\n" ); document.write( "\n" ); document.write( "Find a formula for the balance B after t monthly payments. \n" ); document.write( "
Algebra.Com's Answer #797804 by Theo(13342)\"\" \"About 
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the interest charge is 9.6% per year.
\n" ); document.write( "payments are usually monthly, with monthly compounding assumed.
\n" ); document.write( "the interest 9.6% per per year is divided by 12 to get an interest rate of 9.6/12 = .8% per month.
\n" ); document.write( "the formula uses the rate, not the percent.
\n" ); document.write( "without any payments, the balance at the end of each month is the balance at the end of the previous month times 1.008.
\n" ); document.write( "your minimum payment per month is 3% of the remaining balance.
\n" ); document.write( "you would first multiply the remaining balance from the previous month by 1.008 and then multiply that by (1 - .03) = .97.
\n" ); document.write( "the net effect is to multiply the remaining balance from the previous month by 1.008 and then multiplying it by .97.
\n" ); document.write( "the composite rate is therefore 1.008 * .97 = .97776.
\n" ); document.write( "the remaining balance at the end of each month will be .97776 times the remaining balance for the previous month.
\n" ); document.write( "at the end of the first month:
\n" ); document.write( "2600 * .97776 = 2541.176
\n" ); document.write( "at the end of the second month:
\n" ); document.write( "2541.176 * .97776 = 2485.638006
\n" ); document.write( "at the end of the third month:
\n" ); document.write( "2485.638006 * .97776 = 2430.357417
\n" ); document.write( "this continues at the end of any month of the loan.
\n" ); document.write( "the formula for the balance at the end of any month is:
\n" ); document.write( "Bn = 2600 * .9776 ^ n
\n" ); document.write( "Bn is the remaining balance for the end of the month indicated.
\n" ); document.write( "using this formula, you see that B3 = 2600 * .97773 ^ 3 = 2430.357417.
\n" ); document.write( "this is the remaining balance at the end of the third month as indicated earlier.
\n" ); document.write( "this proves that the formula can provide you with the balance at the end of any month indicated.
\n" ); document.write( "replace n with t and the formula is:
\n" ); document.write( "Bt = 2600 * .97776 ^ t
\n" ); document.write( "that is the formula for the balance B after t monthly payments.
\n" ); document.write( "use that formula to find the balance at the end of 5 monthly payments.
\n" ); document.write( "Bt = 2600 * .97776 ^ t becomes B5 = 2600 * .97776 ^ 5 = 2323.457216.
\n" ); document.write( "start with end of month 3 balance from above.
\n" ); document.write( "at the end of the third month:
\n" ); document.write( "2485.638006 * .97776 = 2430.357417
\n" ); document.write( "at the end of the fourth month:
\n" ); document.write( "2430.357417 * .97776 = 2376.306268
\n" ); document.write( "at the end of the fifth month:
\n" ); document.write( "2376.306268 * .97776 = 2323.457216.
\n" ); document.write( "the formula accurately reflects the remaining balance after t payments.\r
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\n" ); document.write( "\n" ); document.write( "i'll be available to answer any questions you might have about this.
\n" ); document.write( "theo \n" ); document.write( "
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