Question

You have just sold your house for $1,050,000 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 18.5 years​ old, and you have just made a payment. If the interest rate on the mortgage is 5.25% ​(APR with​ semi-annual compounding), 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.)

a.  Compute the discount rate for the mortgage. (4 decimals)

b.  Compute the mortgage payments. (4 decimals)

c.  Compute the remaining balance on the mortgage. (4 demicals)

d.  Find the cash from the sale once the mortgage has been paid off. (4 demicals)

Answer 1

Part (a):

Discount rate of the mortgage: APR of 5.25% compounded semi annually is equal to monthly rate of 0.4328% as follows:

Part (b):

Monthly mortgage payment= $ 3,840.9583 as follows:

Part (c):

Remaining balance in the mortgage after 18.5 years is the PV of remaining installments

= $ 398453.1185 as follows:

Part (d):

Sale value= $1,050,000

Cash from sale after paying off the mortgage= $1,050,000-$398453.118480 = $651,546.8815