Question

An investor obtained a fully amortizing mortgage five years ago for $175,000 at 11.5% for 30 years. Mortgage rates have dropped so that a fully amortizing 20-year loan can be obtained at 10%. There is no prepayment penalty on the mortgage balance of the original loan, but 3 points will be charged on the new loan and other closing costs will be $3000. All payments are monthly. What is the effective "return" earned by the investor if he refinances?

Answer 1

According to the above-given question the solution follows as that

Original Mortgage:-

Value $175,000  
Number of years 30  
Interest per annum 11.50%  
Number of years left 20  

Payment per month   $1,733.01   =PMT(11.5%/12,30*12,-$175,000)

Mortgage value after 10 years (30 years original mortgage - 20 years left)  

$162,505.80   =PV(11.5%/12,20*12,-$1,733.01)

Refinancing to New Mortgage:-

New Mortgage Amount $162,505.80
Charges on new loan (3%) $4,875.17 ($162,505.8*3%)
Closing costs $3,000.00  
Total Closing costs $7,875.17 ($4,875.17+$3,000)
Net New Mortgage Loan $154,630.63 ($162,505.8-$7,875.17)
Number of years 20  
Interest per annum 10%  

Payment per month

$1,568.22   =PMT(10%/12,20*12,-$162,505.80)

Effective Return per annum if he refinances

10.73%  =RATE(20*12,-$1,568.22,$154,630.63)*12