anonymous
  • anonymous
Marcie has a 30 year adjustable rate mortgage with a fixed rate for the first 5 years. In the 6th year, the interest rate rises to 4.9%. The remaining balance at the end of the 5th years is $317,783.30. What is the monthly payment in the 6th year?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
$1,686.56 $1,059.26 $1,878.56 $1,839.26
tkhunny
  • tkhunny
You do know that you can just ignore most of the information? What we need is the payment for a 25 year mortgage @ 4.9% interest on an original balance of $317,783.30. If i = 0.049 j = i/12 v=1/(1+j) The \(Pmt = 317783.30\cdot \dfrac{1-v}{1-v^{301}}\)
anonymous
  • anonymous
i=30 ?

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tkhunny
  • tkhunny
?? I did not explain sufficiently clearly. The fact that we started with a 30-year ARM has no bearing whatsoever on the present payment requirements. All that we need to concern ourselves with is what is left. There are only 25 years left. Paying monthly, this gives 25*12 = 300 more payments. The formula needs one more (it's just the way it is in this form). Thus, 301 is correct. Please note that the provided definition of 'v' is a MONTHLY definition. There are other ways to write the formula so that it is 300, rather than 301. This is of no concern. It's just algebra.
tkhunny
  • tkhunny
Whoops!! Got it wrong. The denominator in this form should be "\(v - v^{301}\)". Sorry about that.
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=317783.30*%28v-v%29%2F%28v-v%5E%28301%29%29
anonymous
  • anonymous
hold on..
tkhunny
  • tkhunny
Did you define v?
anonymous
  • anonymous
v=1/(1+12) ?
tkhunny
  • tkhunny
No. Look up above. i = 0.049 j = i/12 v = 1/(1+j) Follow the path. You have to convert it to monthly compounding.
anonymous
  • anonymous
v=1/(1+0.004083333)?
tkhunny
  • tkhunny
That's it. Why do you doubt?
anonymous
  • anonymous
making sure its not wrong
tkhunny
  • tkhunny
Well, it's not pretty; that's for sure.
anonymous
  • anonymous
v=0.995933273
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=317783.30*%280.995933273-0.995933273%29%2F%280.995933273-0.995933273%5E%28301%29%29
tkhunny
  • tkhunny
Look at the numerator. Why would it be anything but zero. Fix that first one. It's "1-v", not "v-v". They are both v's in the denominator. They are not both v's in the numerator.
tkhunny
  • tkhunny
I should type it correctly, just for the record. i = 0.049 j = i/12 v=1/(1+j) \(Pmt = 317783.30\cdot\dfrac{1−v}{v−v^{301}}\)
anonymous
  • anonymous
o.O
tkhunny
  • tkhunny
Did we get it or did I forget some ARM concept that should have been included?
tkhunny
  • tkhunny
You should also note that 317783.30*0.049/12 = 1297.62 - This is the initial monthly interest, starting in year 6. Anything less than this would not pay off the loan at all!
anonymous
  • anonymous
M=B[((i)(1+i)^(n*t))/((1+i)^(n*t)-(1)) can I use that formula ?
anonymous
  • anonymous
I go it !http://www.wolframalpha.com/input/?i=317%2C783.30%5B%28%280.004083333%29%281%2B0.004083333%29%5E%2812*30%29%29%2F%28%281%2B0.004083333%29%5E%2812*30%29-%281%29%29
anonymous
  • anonymous
the answer is >>> $1,686.56
tkhunny
  • tkhunny
Sorry, but that makes no sense. Why is the time horizon 30 years at the end of year 5? I agree, if we start over another 30 years, we get $1,686.56. Why would we start over? Makes no sense at all.

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