Question 1109824
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L = amount of money loaned out (principal)
L = 85% of initial home value (since 15% is already paid down)
L = 85% of $70,391
L = 0.85*70391
L = 59832.35
So the mortgage balance starts at $59,832.35 (this is the amount of money loaned to the couple)


The annual interest rate is r = 9.3% = 0.093
The monthly interest rate is c = r/12 = 0.093/12 = 0.00775


The mortgage is set for y = 15 years, which is n = 12*y = 12*15 = 180 months

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I'm going to use the second formula mentioned on <a href="https://www.mtgprofessor.com/formulas.htm">this page</a>


The formula mentioned is {{{B = (L*((1+c)^n-(1+c)^P))/((1+c)^n-1)}}}
which will help us find the balance B after the number of months p


So we'll plug in...
L = 59832.35
c = 0.00775
n = 180
p = 108
and that leads us to the balance being...
{{{B = (L*((1+c)^n-(1+c)^p))/((1+c)^n-1)}}}


{{{B = (59832.35*((1+0.00775)^180-(1+0.00775)^108))/((1+0.00775)^180-1)}}}


{{{B = 33980.2387672002}}}


{{{B = 33980.24}}}
So the balance after the 108th payment is $33,980.24


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A = Appraised Value
A = 100,000
B = Balance on mortgage (aka: amount of money still needed to be paid back)
B = 33,980.24 (calculated above)
E = Home Equity Value
E = A - B
E = 100,000 - 33,980.24
E = 66,019.76


We now know the home equity value. So we simply take 70% of this to find the max loan amount
70% of E = 0.7*E = 0.7*66019.76 = 46,213.832 = 46,213.83
which rounds to 46,214 when rounding to the nearest dollar


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Final Answer: <font color=red>$46,214</font>

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