SOLUTION: 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

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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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