Question

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

13

years ago for

​60,634.

The home was financed by paying

15​%

down and signing a 15​-year

mortgage at

8.1​%

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

156th

​payment, they applied to the loan company for the maximum loan. How much​ (to the nearest​ dollar) will they​ receive?

Answer 1

Home was purchased 13 years ago for $60,634

At that point in time, 15% was paid as downpayment. So 15%*60634 = $$9,095.1 was paid as a downpayment. Rest was financed @8.1%. Amount of loan being $51,538.9

Lets calculate the per month payment with these loan conditions. Input the following in the financial calculator.

FV = 0; PV = 51538.9, n = 12*15; 1/y = 8.1%/12; calculate PMT = $495.51

Now, after 156th payment, we need to calculate the outstanding loan balance. After paying 156th installment, only 24 installment remains.

Input the following in the financial calculator to calculate the principle outstanding at the end of 156th payment

FV = 0; PMT = 495.51, 1/y = 8.1%/12, n=24; calculate PV = $10,945.01

Now, it means out of total $51,538.9 loan, only $10,945.01 is outstanding.

Now market value of the home is $100,000, so the Equity in home is $100,000 - $10,945.01 = $89,055

So maximum loan which they can apply is for 70% of Equity = 70%*$89,055 = $$62,338.5