Question

You have just sold your house for $ 1 comma 000 comma 000 in cash. Your mortgage was originally a​ 30-year mortgage with monthly payments and an initial balance of $ 800 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 5.25 % ​(APR), how much cash will you have from the sale once you pay off the​ mortgage? g

Answer 1

cash received = $510194.55

Step-by-step explanation:

given data

sold your house = $1000000

time t = 30 year = 360 month

initial balance P = $800,000

mortgage currently exactly​ = 18½ years = 138 months

interest rate r = 5.25 % = 0.525% per month

solution

first, we will get monthly loan payment is express as

C = P ÷
`(1)/(r) * (1-(1)/((1+r)^n))` ...............1

Put here values

C = 800,000 ÷
`(1)/(.00525) * (1-(1)/((1+0.00525)^(360)))`

C = $ 4951.78

so that monthly payment is $ 4951.78

and

Balance after the 18.5 years will be

Balance = $ 4951.78 ×
`(1)/(0.00525)` ×
`(1-(1)/(1.00525^(138)))`

Balance after 18.5 year = $ 485287.64

Balance after 18.5 year = $489805.45

but here we received here $1000,000 excess cash received is

so

cash received = 1000,000 - 489805.45

cash received = $510194.55