## Related questions with answers

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?

Solution

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

The amortisation was for 30 years. Let $P$ be the unpaid balance after $120^{th}$ 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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