Question 1109824: A couple wishes to borrow money using the equity in their home for collateral. A loan company will loan them up to 70% of their equity. They puchased their home 9 years ago for $70,391. The home was financed by paying 15% down and signing a 15-year mortgage at 9.3% on the unpaid balance. Equal monthly payments were made to amortize the loan over the 15-year period. The net market value of the house is now $100,000. After making their 108th payment, they applied to the loan company for the maximum loan. How much (to the nearest dollar) will they receive?
Thank you in advance.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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 this page
The formula mentioned is 
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...
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: $46,214
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