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 $700,000. 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.)

Answer 1

Solution:-

Firstly we have to calculate the monthly effective rate;

rate = 7.75%

monthly rate = 7.75%/12 = 0.645833%

n= 30 * 12 = 360 months

Monthly payment = (payment * r) / [1-1/(1+r)ⁿ]

= (700,000 * 0.006458) / [1-1/(1+0.006458)³⁶⁰]

= 4,520.6 / [1-1/10.1493]

= 4,520.6 / 0.901471

= 5,014.6926

Solving the loan amount outstanding,we will use PV formula

n= 11.5 * 12 = 138 months

PV = (5,014.6926 / 0.006458) * (1-1/1.006458¹³⁸)

= 776,508.6175 * 0.58866

= 457,099.56

So, you would keep $900,000 - $489,774.96 = $442,900.44