Question

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?

Answer 1

Answer:

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 ÷   $\frac{1}{r} \times (1-\frac{1}{(1+r)^n})$      ...............1

Putting values in formula we get

C = 750,000 ÷  $\frac{1}{.00646} \times (1-\frac{1}{(1+0.00646)^{360}})$  

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  × $\frac{1}{0.00646}$   ×  $(1-\frac{1}{1.00646^{138}})$      

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