Question

You have just sold your house for 900,000 in cash. Your mortgage was originally a​ 30-year mortgage with monthly payments and an initial balance of $750,000. The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 7.75% ​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Cash that remains after payoff of mortgage is

​$____

Answer 1

Amount borrowed				750000
Annual rate				7.75%
Monthly rate (7.75/12) = 0.65%
Annuity PVF at 0.65% for 360 periods				138.9139
Monthly payment (750000/138.91387)				5399.03
Monthly periods paid = 18.5*12				222
Remaining period left		(360-222)		138
Annuity PVF at 0.65% for 138 periods				90.92668
Loan amount outtstanding at date of sale				490915.9
	(5399.03*90.92668)
Price received at the date of sale				900000
Net amount left in hand = 900000- 490915.9 = 409084.1
Answer is $ 409084.1