You have just sold your house for $ 1000000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $ 750 comma 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?

cash will you have from the sale once you pay off the mortgage is $ 510194.55

Explanation:

given data

sold your house = $1000000

time t = 30 year  = 360 month

initial balance P = $750,000

mortgage currently exactly = 18½ years  = 138 months

interest rate r = 7.75 % = 0.646% per month

solution

we get here monthly loan payment  that is

C = P ÷        ...............1

Putting values in formula we get

C = 750,000 ÷    

C = $5374.12

so monthly payment is $5374.12

and here Balance after 18.5 year will be

Balance after 18.5 year  = $5374.12  ×   ×        

Balance after 18.5 year  = $489805.45

and  

we received here $1000,000 excess cash received is

cash received = 1000,000 - 489805.45

cash received = $ 510194.55

the answerr would be 1

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