A couple wishes to borrow money using the equity in their home for collateral. A

Question

A couple wishes to borrow money using the equity in their home for collateral. A loan company will loan them up to 65% of their equity. They purchased their home 20 years ago for $82,000. The home was financed by paying 20% down and signing a 30-year mortgage at 4.5% on the unpaid balance. Equal monthly payments were made to amortize the loan over the 30-year period. The net market value of the house is now $125,000. After making their 240th payment, they applied to the loan company for the maximum loan. Show work by setting up the problem and rounding answer to the nearest penny. How much is their original mortgage? _____ How much are their payments? _____ How much do they still owe after making their 240th payment? _____ How much is their equity? _____ What is the maximum loan that the bank will give them? ____________

Explanation / Answer

Solution:

(i) How much the origional mortgage was;

they financed 80% of $82000;

=> 80% * 82000 = $65600

(ii) figure out their monthly mortgage payment

PMT = PV(r/n) / [1 - (1 + r/n)^(-nt)]

PMT = 65600 (0.045/12) / [1 - (1 + .045/12)^(-12 * 30)]

PMT = 246 / 0.74

PMT = $332.4

(iii) figure out the balance of the mortgage after twenty years (240 pmts)

B = PV(1 + r/n)^(s) - [PMT / (r/n)][(1 + r/n)^(s) - 1]

B = 65600(1 + .045/12)^(12 * 20) - [332.4 / (.045/12)][(1 + .045/12)^(12 * 20) - 1]

B = 161078.59 - 129012.54 = $32066.05

The balance is $32066.05

(iv) House is worth = $125000

Equity is = 125000 - 32066.05 = $92933.95

(v) Maximum loan that the bank will give;

=> Equity * 65% = 92933.95 * 0.65 = $60407.067 = $60407

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