Question

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?

Answer 1

$1,686.56

$1,059.26

$1,878.56

$1,839.26

Answer 2

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 \(Pmt = 317783.30\cdot \dfrac{1-v}{1-v^{301}}\)

Answer 3

i=30 ?

Answer 4

?? 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.

Answer 5

Whoops!! Got it wrong. The denominator in this form should be "\(v - v^{301}\)". Sorry about that.

Answer 6

http://www.wolframalpha.com/input/?i=317783.30*%28v-v%29%2F%28v-v%5E%28301%29%29

Answer 7

hold on..

Answer 8

Did you define v?

Answer 9

v=1/(1+12) ?

Answer 10

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.

Answer 11

v=1/(1+0.004083333)?

Answer 12

That's it. Why do you doubt?

Answer 13

making sure its not wrong

Answer 14

Well, it's not pretty; that's for sure.

Answer 15

v=0.995933273

Answer 16

http://www.wolframalpha.com/input/?i=317783.30*%280.995933273-0.995933273%29%2F%280.995933273-0.995933273%5E%28301%29%29

Answer 17

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.

Answer 18

I should type it correctly, just for the record.

i = 0.049
j = i/12
v=1/(1+j)

\(Pmt = 317783.30\cdot\dfrac{1−v}{v−v^{301}}\)

Answer 19

o.O

Answer 20

Did we get it or did I forget some ARM concept that should have been included?

Answer 21

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!

Answer 22

M=B[((i)(1+i)^(n*t))/((1+i)^(n*t)-(1)) can I use that formula ?

Answer 23

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

Answer 24

the answer is >>> $1,686.56

Answer 25

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.