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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?
What is the monthly interest rate corresponding to the effective annual rate?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Find standard formulas for it in any textbook in finance.
Why do you neglect such simple way to increase the level of your knowledge ?
It would seem that this is the first step you should do when studying this subject, isn't it ?
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! bi-weekly means every 2 weeks, i believe.
since there are 52 weeks in a year, then there are 26 bi-weekly periods in a year.
when compounded bi-weekly, the effective growth factor per year is (1 + .075/26) ^ 26 = 1.077767783.
to find the effective monthly growth factor, you would take the 12th root of the effective yearly growth factor.
you would get an effective monthly growth factor of 1.077737783 ^ 1/12 = 1.006260519.
the trow factor is equal to the interest rate percent divided by 100 and then add 1 to it.
going in reversse, the interest rate percent is the growth factor minus 1 and then being multiplied by 100.
your effective annual growth factor is 1.077767783.
subtract 1 from that and then multiply it by 100 to get 7.7767783% effective annual interest rate percent.
your effective monthly growwth factor is 1.006260519.
subtact 1 from that and then multiply it by 100 to get .6265019% effective monthly interest rate percent.
that should take care of your second question.
as to your first question, .....
your present value is 550,000.
your interest rate per bi-weekly time period is 7.5% / 26 = .2884615385%.
your bi-weekly growth factor is that divided by 100 and then have 1 added to it to get 1.002884615385.
the equivalent monthly growth factor is that raised to 26th power and then taken to the 12th root.
you will get 1.006260519.
subtract 1 from that and then multiply it by 100 to get a monthly interest rate of .6260519 effectivfe monthly interest rate.
the calculator i used is at https://arachnoid.com/finance/
my ijnputs to that calculator were:
preseent value = 550,000
future value = 0
number of time periods = 25 years * 12 months per year = 300 months.
interest rate per time period = .6260519% per month.
payments are made at the end of each month.
the results are shown below.
the payments are calculated to be 4,068.97 payable the end of each month, rounded to the nearest penny.
there are 300 payments, so the total amount of payments = 1,220,691.
the total interest payed is that minus 550,000 = 670,691.
please note that there is some intermediate rounding done when using the onine calculator.
i did the same analysis using the texas intstruments busines analyst 2 calculator and got a monthly payment of 4068.968191.
that gave me a total pyments of 300 * that = 1,220,690.457
subtract 550,000 from that to get total interest of 670,690.4573.
round that to the nearest penny to get 670,690.46.
it's a very small difference, but it is there.
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