# Mortgage Refinance Calculator

#### Mortgage Refinance Calculator Definition:

Mortgage refinancing refers to obtaining a new loan by replacing an existing loan by securing the same assets with different terms. This is the most popular form of loan in home mortgage.

#### Calculator:

Example:

The principal on the existing loan is P = \$98,000 at a current interest rate of 7.5% for 240 months. For this loan the current monthly payments are CP = \$800. A new loan is taken at r =6% interest rate and period m= 120. The closing cost is \$3000. Mortgage refinance calculations and monthly payment for the new loan :

##### using the annuity formula :

NP = P (i (1+i)^m/(1+i)^m -1 )
Substituting the values:
(98000)(.005)(1.005)^120 = 891.5044 and (1.005)^120 – 1= .8194
so NP = 891.5044/.8194 = \$1088
computing the total cost of the refinanced loan
(NP*m) + C = (1088 *120) + 3000 = \$133560
Total cost of the old loan
CP * M = 800 *240 = \$192000

The difference between the old loan value and the new loan value = \$192000 - \$133560 = \$58440

When refinanced under the new terms the money saved in the long run is \$58440
To calculate breakeven point:

Let us suppose a person takes a loan of \$170,000 at the rate of 8% per annum on a 30 year mortgage and he took out after 5 years, then his monthly payment is

170,000((8/100/12*(1+(8/100/12)^360)/ ((1+8/100/12)^360 – 1) = \$1312
If the person refinanced to a new 30 year loan at the rate of 6.5% interest per annum, then the monthly payment is \$1074.53

The difference between the two amounts is \$1312 - \$1074.5 = \$237
If the closing cost is \$4800 then 4800/237 = 20.25
According to the formula money can be saved in less than 21 months.