Question

A homeowner took out a 25-year, fixed-rate mortgage of $210,000. The mortgage was taken out 8 years ago at a rate of 7.1 percent. If the homeowner refinances, the charges will be $3,400. What is the highest interest rate at which it would be beneficial to refinance the mortgage? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

APR% _____

Answer 1

Given data, 25 year term loan @7.1 percent and it is now end of 8 years.

The present loan balance as per the repayment schedule i.e., principal amount due is 177148/-

Assuming the rate to be monthly compounding,

The present EMI comes to 1497.66 I.e., monthly payment.

Now the amount to be refinanced is the loan amount and the additional cost of refinancing I.e.,3400 that amounts to $180548/-

Such new loan to be amortized over balance period of 17 years.

In order to decide whether to go for refinancing or not depends upon our savings in comparison with earlier loan payments. Earlier we used to pay $ 1497/ month and if we are able to close the loan with lower payments within the same time schedule of remaining 17 years we can opt for refinancing.

The question now is regarding the maximum rate at which refinancing can be opted. To answer this, we need to equate the new loan of $180548/- to the present value of monthly payment of $1497.67/- at a rate for the balance period of 17 years.

Such rate is the maximum rate of interest at which refinancing can be at break even position. And any rate below this can be beneficial.

Therefore, $1497.66*PVAF(R% , 204) =$180548/-

If. We solve this we get R% = 6.82% is the maximum rate at which refinancing can be opted.