Simple word problem. I guess me public school education has failed me.
Should be the easiest $10 you ever made.
Everything in this equation does NOT include taxes and insurance. 
My Mother takes out a mortgage from the bank for $85,000 at 6%
interest.
My Mother loans me $113,000 at 7% interest.
Obviously, she is making 1% on the original $85,000 for doing nothing.
What interest rate is she making on the true cash part of the
difference? ($113,000 minus $85,000 equals $28,000)
The following example should help.
The $85,000 comes out to $509.62 that she would pay monthly to the
bank.
I would pay $751.79 per month to her for $113,000 at 30 years.
So, there is $242.17 a month for her in interest and prinicle for the
$28,000.
I would think a reverse calculator where you plug in the monthly
amount and the years and the starting balance and END up with the
interest rate would do it.
But wait, I even already screwed up. I took the difference when that
is not correct. The 1% difference between 6% and 7% got factored in
the above.
You should have enough information even with my misinformation above.

All of this assume a 30 year ammoritization.
Please include the link to a calculator so I can change these numbers
myself.

Hi kaiserwilhelm!!

Donīt worry about your education, sometimes the problems are more
difficult that they seem to be.


As your mother has to pay $509.62 monthly to the bank for $85,000 at
6% interest, I see that the bank deals with the French System of
Amortization.

Its formula is the following:

       VA * i
C=_______________
   1 - (1+i)^(-n)

Where

C: amount that your mother has to pay monthly to the bank. ($ 509.62)
VA: amount of the mortgage your mother takes out from the bank. ($
85,000)
i: the anual interest that your mother has to pay for the mortgage
(6%)
n: quantity of periods or quotas of the mortgageīs repayment.(30
years)

Replacing with the figures you inform, we have:

VA= 85,000
i= 0.06 / 12 months (as you have a monthly amount) = 0.005
n= 30 years * 12 months (we have to pass everything to months)= 360

And the formula would be

  85,000 * 0.005		       425
____________________ = __________________ = 509.6179 

1- (1+0.005) ^(-360)      1- 0.1660419


If your mother has $ 28,000 to lend you and if she has pay nothing for
this amount because it is saved money, she is making the interest of 7
%. So, all the amount that you would pay monthly, if you take out a
mortgage from some bank for $28,000 at 7% interest, would be your
motherīs income.

In this way, your mother will earn for the $28,000 the total (C) that
give us the  formula above with the following figures:

VA= 28,000
i= 0.07 / 12 = 0.0058333
n= 360

        28,000 * 0.0058333	     163.3333
 C = ________________________ = __________________ = 186.28469

     1- (1+0.0058333) ^(-360)      1- 0.12320585

The difference between $242.17, that you observe, and this $186.28 is
$55.89, this is the 1% that she is making on the original $85,000 for
doing nothing.
(Your mother is buying money at 6% to sell you at 7%, like every bank
do).

In effect, for the rest $85,000 that your mother lends you, she
obtains (at 7%):

         85,000 * 0.0058333	     495,8333
 C = ________________________ = __________________ = 565.5071209023

     1- (1+0.0058333) ^(-360)      1- 0.12320585

But, for this $85,000 she has to pay to the bank $509.6179

So, for the $85,000 she earns the difference between $565.51 and
$509.62, that is the $55.89 that I mentions above.

In conclusion we can split your payment of $751.79 in two parts:

The first part is a payment of $565.51 from where your mother obtain a
monthly rent of $55.89 (that is the difference between $565.51 and
$509.62).
The second part is a payment of $186.28, that is all for your mother,
this corresponds to a payment for a mortgage of $28000 with the 7% of
interest rate.
Then the difference between your payment and your mother payment
($242.17) can be splited in two:
$55.89 that corresponds to the 1% of rent for the $85000;
$186.28 that corresponds to the loan of $28000 with 7% of interest
rate.


This problem was solved using my own knowledge.

I hope this helps you, if you need a clarification, please feel free
to post a request for it.

Best regards.
livioflores-ga