Question 1109697: Hello Tutors, I will appreciate it if you help me solve this question. Thank you in advance.
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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! original price of the home was 70,391.
owner paid 15% down and took out a mortgage for the rest.
70,391 - .15 * 70,391 = .85 * 70,391 = 59,832.35.
mortgage was for 15 years at 9.3% compounded monthly.
use a financial calculator and make the following entries:
present value = 59,832.35.
futuve value = 0
number of months = 15 * 12 = 180
interest rate percent per month = 9.3/12 = .775 percent per month.
select payments made at the end of each month.
compute payment.
payment will be -617.5836941 per month.
it will show up as negative because the present value was positive.
positive is money coming in.
negative is money going out.
your monthly payments are going out from you, therefore negative.
108 payments have been made when you want to apply for the home financing loan.
that means that 180 - 108 = 72 payments are required to finish the loan.
unless your calculator can tell you what the remaining equity in the home is after 108 payments, then you need to find out what the remaining balance in the home is by using the following method.
put the following information in your financial calculator.
future value = 0
interest rate = .775% per month.
payments made at the end of each month.
payment per month = -617.5836941
number of months = 72
compute present value.
calculator will tell you that the present value is 33,980.23877.
that's the remaining equity in your home.
it's the amount that you still owe to the bank in order to pay off the 15 year mortgage completely.
your home is now worth $100,000.
take out what you still owe on the house and you are left with 100,000 - 33,980.23877 = 66,019.76123.
that's the remaining equity in your home based on net market value of the home being 100,000 at the time you apply for the loan.
70% of 66,019.76123 = 46,213.83186.
round that to 46,214 and that's the amount of money you can borrow.
i believe this is correct, but i don't work for a bank and so can't be 100% sure i did it right, although i will vouch for the calculations involved based on my assumptions.
i used the following reference to come up with the equity being the current market value of the house minus any liens on it, such as remaining balance on a mortgage.
https://en.wikipedia.org/wiki/Home_equity
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