You have a $200,000 mortgage. You have had the house for one year. The rate is 7.5% fixed for 30 years. Rates have come down and you are thinking of refinancing at the new rate of 6%.
1) What is your mortgage payment and interest on your current mortgage?
2) What would your new mortgage payment, principal and interest be if you refinanced?
3) What is your monthly savings?
first we need the payment of the original mortgage
i = .075/12 = .00625
n = 12(30) = 360
p(1 - 1.00625^-360)/.00625 = 200,000
I got p = 1398.43
1) the payment is $1398.43 , and the interest will depend on what payment period you are talking about. I will change.
2. We need the outstanding balance at the end of one year
amount = 200000(1.00625)^12 - 1398.43(1.00625^12 - 1)/.00625
= 198156.33
new rate = .06/12 = .005
new n = 348
new payment P
P(1 - 1.005^-348)/.005 = 198156.33
I got P = 1202.82
3. Saving in monthly payment
= 1398.43 - 1202.82
= 195.61
To calculate the current mortgage payment and interest, we need to use the mortgage formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where:
M = monthly payment
P = principal balance (in this case, $200,000)
i = monthly interest rate (7.5% divided by 12, or 0.075 / 12)
n = number of payments (30 years multiplied by 12, or 30 x 12)
1) To find the current mortgage payment, plug the values into the formula:
M = 200,000 [ 0.00625(1 + 0.00625)^360 ] / [ (1 + 0.00625)^360 – 1]
By calculating this formula, the current mortgage payment is approximately $1,398.57.
The interest paid on the current mortgage can be determined by multiplying the monthly payment by the total number of payments (360 for a 30-year mortgage) and subtracting the principal balance:
Interest = (M x n) - P
Interest = ($1398.57 x 360) - $200,000
Interest = $254,485.20 - $200,000
Interest = $54,485.20
Thus, the interest paid on the current mortgage is $54,485.20.
To calculate the new mortgage payment and principal and interest after refinancing, we again use the mortgage formula, but with the new interest rate of 6%.
2) Plug the new interest rate into the formula:
M = 200,000 [ 0.005(1 + 0.005)^360 ] / [ (1 + 0.005)^360 – 1]
By calculating this formula, the new mortgage payment after refinancing is approximately $1,199.10.
The principal and interest can be obtained by multiplying the new monthly payment by the total number of payments and subtracting the principal balance again:
Principal and Interest = (M x n) - P
Principal and Interest = ($1199.10 x 360) - $200,000
Principal and Interest = $431,676.00 - $200,000
Principal and Interest = $231,676.00
The new mortgage payment, principal, and interest after refinancing would be approximately $1,199.10, and the principal and interest would be $231,676.00.
3) To calculate the monthly savings, subtract the new mortgage payment from the current mortgage payment:
Monthly Savings = Current Mortgage Payment - New Mortgage Payment
Monthly Savings = $1,398.57 - $1,199.10
Monthly Savings = $199.47
Therefore, the monthly savings after refinancing would be approximately $199.47.