A homeowner has $200,000 home with a 20-year mortgage, paid monthly at a quoted

Question

A homeowner has $200,000 home with a 20-year mortgage, paid monthly at a quoted interest rate of 7.25% per year compounded semi-annually. After five years he receives $50,000 as an inheritance. If he pays this $50,000 toward his mortgage along with his regular payment, by approximately how many years will it reduce the amount of time it takes him to pay off his mortgage? Five years ago you took out a 30-year mortgage with a quoted interest rate of 6.5% per year compounded semi-annually for $200,000. If you were to refinance the mortgage today for 20 years at a quoted rate of 4.25% per year compounded semi-annually, how much would you save in total interest expense?

Explanation / Answer

Part 3)

The future value of the mortgage after 30 years can be calculated with the use of following formula:

Future Value = Amount of Mortgage*(1+Rate)^n

__________

Step 1: Calculate Interest Expense with Initial Mortgage Information:

Amount Payable after 30 Years = 200,000*(1+6.50%/2)^(30*2) = $1,362,804.68

Total Interest with Initial Option = 1,362,804.68 - 200,000 = $1,162,804.68

__________

Step 2: Calculate Interest Expense with Revised Mortgage Information:

Amount Today (After 5 Years) = 200,000*(1+6.50%/2)^(5*2) = $275,378.86

Amount Payable after 20 Years at 4.25% = 275,378.86*(1+4.25%/2)^(20*2) = $638,577.16

Total Interest with Revised Option = 638,577.16 - 200,000 = $438,577.16

__________

Step 3: Calculate Savings in Interest Expense:

Savings in Interest Expense = Interest in Step 1 - Interest in Step 2 = 1,162,804.68 - 438,577.16 = $724,227.52 (answer)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.