document.write( "Question 1201414: Suppose you take out a mortgage for $550000 at 7.5% interest per year compounded bi-weekly. If your mortgage is amortized over 25 years, what is your monthly mortgage payment? How much interest will you pay the lender by the end of the mortgage?
\n" ); document.write( "What is the monthly interest rate corresponding to the effective annual rate? \n" ); document.write( "
Algebra.Com's Answer #835785 by Theo(13342)\"\" \"About 
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bi-weekly means every 2 weeks, i believe.
\n" ); document.write( "since there are 52 weeks in a year, then there are 26 bi-weekly periods in a year.
\n" ); document.write( "when compounded bi-weekly, the effective growth factor per year is (1 + .075/26) ^ 26 = 1.077767783.
\n" ); document.write( "to find the effective monthly growth factor, you would take the 12th root of the effective yearly growth factor.
\n" ); document.write( "you would get an effective monthly growth factor of 1.077737783 ^ 1/12 = 1.006260519.
\n" ); document.write( "the trow factor is equal to the interest rate percent divided by 100 and then add 1 to it.
\n" ); document.write( "going in reversse, the interest rate percent is the growth factor minus 1 and then being multiplied by 100.
\n" ); document.write( "your effective annual growth factor is 1.077767783.
\n" ); document.write( "subtract 1 from that and then multiply it by 100 to get 7.7767783% effective annual interest rate percent.
\n" ); document.write( "your effective monthly growwth factor is 1.006260519.
\n" ); document.write( "subtact 1 from that and then multiply it by 100 to get .6265019% effective monthly interest rate percent.
\n" ); document.write( "that should take care of your second question.
\n" ); document.write( "as to your first question, .....
\n" ); document.write( "your present value is 550,000.
\n" ); document.write( "your interest rate per bi-weekly time period is 7.5% / 26 = .2884615385%.
\n" ); document.write( "your bi-weekly growth factor is that divided by 100 and then have 1 added to it to get 1.002884615385.
\n" ); document.write( "the equivalent monthly growth factor is that raised to 26th power and then taken to the 12th root.
\n" ); document.write( "you will get 1.006260519.
\n" ); document.write( "subtract 1 from that and then multiply it by 100 to get a monthly interest rate of .6260519 effectivfe monthly interest rate.
\n" ); document.write( "the calculator i used is at https://arachnoid.com/finance/
\n" ); document.write( "my ijnputs to that calculator were:
\n" ); document.write( "preseent value = 550,000
\n" ); document.write( "future value = 0
\n" ); document.write( "number of time periods = 25 years * 12 months per year = 300 months.
\n" ); document.write( "interest rate per time period = .6260519% per month.
\n" ); document.write( "payments are made at the end of each month.
\n" ); document.write( "the results are shown below.
\n" ); document.write( "
\n" ); document.write( "the payments are calculated to be 4,068.97 payable the end of each month, rounded to the nearest penny.
\n" ); document.write( "there are 300 payments, so the total amount of payments = 1,220,691.
\n" ); document.write( "the total interest payed is that minus 550,000 = 670,691.
\n" ); document.write( "please note that there is some intermediate rounding done when using the onine calculator.
\n" ); document.write( "i did the same analysis using the texas intstruments busines analyst 2 calculator and got a monthly payment of 4068.968191.
\n" ); document.write( "that gave me a total pyments of 300 * that = 1,220,690.457
\n" ); document.write( "subtract 550,000 from that to get total interest of 670,690.4573.
\n" ); document.write( "round that to the nearest penny to get 670,690.46.
\n" ); document.write( "it's a very small difference, but it is there.\r
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