Suppose a homeowner has an existing mortgage loans with these terms:

Remaining Balance: $150,000
Interest Rate: 8%
Remaining Term: 10 years (monthly payments)

This loan can be replaced by a loan at an interest rate of 6%, at a cost of 3% of the outstanding loan amount.

What is the net benefit(cost) to refinance?

Using a loan calculator we can determine the current monthly payment:

principal = $150,000

APR = 8%

n = 10 years

payment = ? = $1,819.91

total interest charged during the 10 years = $68,389.67

A bank may offer you to refinance your loan at a 3% cost, and that amount is added to the principal, then we can calculate the monthly payments and total interest charged:

principal = $154,500

APR = 6%

n = 10 years

payment = ? = $1,715.27

total interest charged during the 10 years = $51,332.01

Another option you might get is to refinance your loan at a 3% cost, and pay the $4,500. Then we can calculate the monthly payments and total interest charged:

principal = $150,000

APR = 6%

n = 10 years

payment = ? = $1,665.31

total interest charged during the 10 years = $49,836.90

depending on your bank and what refinancing option they give you, you might end up saving a lot of money:

option 1: refinancing costs are added to the principal ⇒ save $12,557.66

after the 10 years you will pay a total of $205,832.01, which is $12,557.66 lower than your current mortgage (= $218,389.67 - $205,832.01), plus you get a lower monthly payment.

option 2: refinancing costs are paid upfront ⇒ save $14,052.77

after the 10 years you will pay a total of $199,836.90 + $4,500 = $204,336.90, which is $14,052.77 lower than your current mortgage (= $218,389.67 - $204,336.90), plus you get a lower monthly payment. The downside is that you need the $4,500 to pay for the refinancing fees.

the answer to this question would be shared investment