Finance math problem

[Sisi]

Hallo!

I would like to ask for your help regarding the following task:

You have been living in the house you bought 10 years ago for $300,000. At that time, you took out a loan for 80% of the house at a fixed rate 15-year loan at an annual stated rate of 9%. You have just paid off the 120th monthly payment. Interest rates have meanwhile dropped steadily to 6% per year, and you think it is finally time to refinance the remaining balance. But there is a catch. The fee to refinance your loan is $4,000. Should you refinance the remaining balance? How much would you save/lose if you decided to refinance?

I know that I have to compare the present values of both cases. I tried solving the task using a time line, but this didn't help. I guess the change in the interest is the main reason for my confusion.

:???:​

I would really appreciate it if you could give me some hints of how to get the right answer.

 

[Ishuda]

Hallo!

I would like to ask for your help regarding the following task:

You have been living in the house you bought 10 years ago for $300,000. At that time, you took out a loan for 80% of the house at a fixed rate 15-year loan at an annual stated rate of 9%. You have just paid off the 120th monthly payment. Interest rates have meanwhile dropped steadily to 6% per year, and you think it is finally time to refinance the remaining balance. But there is a catch. The fee to refinance your loan is $4,000. Should you refinance the remaining balance? How much would you save/lose if you decided to refinance?

I know that I have to compare the present values of both cases. I tried solving the task using a time line, but this didn't help. I guess the change in the interest is the main reason for my confusion.

:???:​

I would really appreciate it if you could give me some hints of how to get the right answer.

Compute
-Original payments p_o
-What you owe right now (after the 120th payment), call it P.
-New payments assuming a 5 year mortgage at 6% and a principle of P, call the new payment p_n

So what is your break even time (in months), i.e. how long will it take for the new payments to pay back the $4000 fee. What if it is negative? What if it is positive but more than 60?

 

[Sisi]

It is not a real life problem, it is just a task.

I need more scientific approach so that I can prove that I will pay less and I have to find the difference.

That's what I have so far:

PMT for the first 120 months is 3 040.22 (calculated with Excel using the formula "=PMT(0.09/12,120,240000)")

Then I found the FV at the 120th month ("=FV(0.09/12,120,0,240000)") to be 588 325.70

After that I take this value for my PV(not sure whether it works this way!) and then calculate the PMT with the new interest to be 11 373.98

Then I just calculate the difference at point 120th by using the PMT values (and I add these 4000 which have to be paid if refinance occur to the second case's final result) and I get a difference of 121 543.5! That is definitely wrong.

 

[jonah2.0]

WARNING: Beer soaked rambling/opinion/observation ahead. Read at your own risk. Not to be taken seriously. In no event shall Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.

Is this a class assignment, or real life?

Quickly:
the present monthly payment is 2,434
if renewed @ 6%, payment will be 2,267 (last 5 years)
2434 - 2267 = 167 : 167 * 60 = 10,020
So it's sure worth paying 4,000

If you need something different or more precise, come back
and tell us exactly what you need...and show your work if this is homework...

Lovely Sir Denis, just lovely.
I was just watching Yosemite Sam in Dumb Patrol and it suddenly occurred to me that you deserve nothing less than a red cross for shooting down this flying dragon.
Although I'm not sure I'd agree with your treatment of the refinancing penalty fee of $4,000; roughly equal to 164.32% of a month's payment.
Shouldn't you add that to the outstanding balance after the 120th payment to calculate the new monthly payment for a reduced total interest payment of about $9,390.40?
No worries. Still the same decision.

 

[jonah2.0]

WARNING: Beer soaked rambling/opinion/observation ahead. Read at your own risk. Not to be taken seriously. In no event shall Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.

A RED CROSS! And after I awarded you earlier a cheap red star for your forehead :shock:
Your generosity knows no bounds...

My bad.
Meant to type "iron cross".
Too drunk as usual.