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A person purchased a house 10 years ago for $160,000. The house was financed by paying 20% down and signing a 30-year mortgage at 7.75% on the unpaid balance. Equal monthly payments were made to amortize the loan over a 30-year period. The owner now (after the 120th payment) wishes to refinance the house due to a need for additional cash. If the loan company agrees to a new 30-year mortgage of 80% of the new appraised value of the house, which is$225,000, how much cash (to the nearest dollar) will the owner receive after repaying the balance of the original mortgage?

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The equity of the couple in house would be equal to the share of present value that has been paid (including down payment) after 120th120^{th} payment (12 years ).

The amortisation was for 30 years. Let PP be the unpaid balance after 120th120^{th} payment. We know that after 20 years of payment, if the couple continues paying the same amount, this unpaid balance would be paid.

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