Question

Your 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 $825,000.

The mortgage is currently exactly 18.5 years​ old, and you have just made a payment. If the interest rate on the mortgage is 7.75%(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. What is the discount rate for the​ mortgage?

The discount rate for the mortgage is ——%. (Round to four decimal​ places.)

Answer 1

APR(monthly) = 12[(1 + 0.0775/2)1/6 - 1]

APR(monthly) = 7.6278%

Discount Rate = 7.6278%

Calculating Monthly Payment,

Using TVM Calculation,

PMT = [PV = 825,000, FV = 0, N = 360, I = 0.076278/12]

PMT = $5,840.89

Calculating Loan Balance after 18.50 years,

Using TVM Calculation,

FV = [PV = 825,000, PMT = -5,840.89, N = 222, I = 0.076278/12]

FV = $535,613.19

Cash Balance after loan repayment = 1,050,000 - 535,613.19

Cash Balance after loan repayment = $514,386.81