document.write( "Question 1192613: A loan of $ 10500 is to be repaid in 43 equal monthly installments with the first one paid seven months after the loan is made. The nominal annual interest rate is 13 % compounded semiannually. Determine the amount of the monthly payment.\r
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Algebra.Com's Answer #824512 by Theo(13342)\"\" \"About 
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the loan amoun is 10,500.
\n" ); document.write( "the interest rate is 13% compounded semi-annually.
\n" ); document.write( "the loan needs to be paid in 43 equal monthly installments.
\n" ); document.write( "the first payment will be made 7 months after the loan is made.\r
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\n" ); document.write( "\n" ); document.write( "the semi-annual interest rate is 13/2 = 6.5%.
\n" ); document.write( "the monthly growth rate is (1.065)^(1/6) = 1.010551074.\r
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\n" ); document.write( "\n" ); document.write( "if you take 1.010551074 and raise it to the 6th power, you will get the semi-annual growth rate of 1.065.
\n" ); document.write( "the semi-annual growth rate of 1.065 minus 1, times 100 = the semi-annual interest rate of 6.5%.\r
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\n" ); document.write( "\n" ); document.write( "the effective annual growth rate is 1.065 ^ 2 = 1.134225.
\n" ); document.write( "it is also 1.010551075 ^ 12 = 1.134225.\r
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\n" ); document.write( "\n" ); document.write( "the effective annual interest rate is 1.134225 minus 1, times 100 = 13.4225%.\r
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\n" ); document.write( "\n" ); document.write( "now that we have the monthly growth rate, we can solve the problem.\r
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\n" ); document.write( "\n" ); document.write( "for the first 6 months, nothing is paid, but the interest is applied to raise the principal from 10500 to 10500 * 1.010551075 ^ 6 = 11182.5.\r
\n" ); document.write( "\n" ); document.write( "that becomes the present value of the 43 month annuity where the payments are equal.\r
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\n" ); document.write( "\n" ); document.write( "you can use a formula, or you can use a calculator.
\n" ); document.write( "the calculator i used is the ti-ba-ii business analyst by texas instruments.
\n" ); document.write( "my inputs to that calculator were:
\n" ); document.write( "present value = 11182.5
\n" ); document.write( "future value = 0
\n" ); document.write( "number of time periods = 43 months.
\n" ); document.write( "interest rate per time period = 1.055107398%
\n" ); document.write( "payments made at the end of each time period.
\n" ); document.write( "i then had the calculator tell me what the monthly payments were.
\n" ); document.write( "it said the payments made at the end of each month were equal to 324.8438861.
\n" ); document.write( "round to the nearest penny to get $324.84.
\n" ); document.write( "that should be your answer.\r
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\n" ); document.write( "\n" ); document.write( "i put the problem in excel to show the monthly transactions and also to confirm the calculations were correct.
\n" ); document.write( "this is what excel showed.\r
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\n" ); document.write( "\n" ); document.write( "excel confirms that the calculations were correct, based on the assumptions that i used.\r
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\n" ); document.write( "\n" ); document.write( "let me know if you have any questions.
\n" ); document.write( "theo
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