Question

You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and had an initial balance of $800,000. 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% p.a. (with monthly compounding), how much cash will you have from the sale once you pay off the mortgage? (Round to the nearest dollar).

a. $456,931 b. $626,635 c. $543,069 d. $540.661 e. $459,340

Answer 1

option c $543,069

Explanation;

Present monthly installment =

Remaining amount after 18.5 years

Ramaining Amount = Formula

Ramaining Amount =

PV= $800,000

payment = $4417.63

Rate = 5.25%/12 = .4375% per month

n = 18.5 years x 12 = 222

= 800,000*(1+.4375%)^222 - 4417.63*[(1+ .4375%)^222 - 1]/.4375%

= 800,000*2.635654576 - 4417.63*[(2.635654576 - 1]/.4375%

=2108523.661 - 4417.63*373.8639031

=2108523.661 - 1651592.394

= $456931.27

House selling amount = $1,000,000

Loan net pay off = $456,931.27

Net cash received after paying loan= $1,000,000 - $456,931.27 = $543,068.73 or $543,069

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