FreddieMac reports that the average rate on a 30-year fixed rate mortgage is 3.92% as of January 2012. This is down from 4.76% in January 2011 and 5.03% in January 2010. If you have a $225,000, 5%, 30-year mortgage, how much interest will you save if you refinance your loan at 3.5% for 15 years?
A. P1 = Po*r*t/(1-(1+r)^-t)
Po = $225,000
r = (5%/12)/100% = 0.004167 = Monthly %
rate expressed as a decimal.
t = 12mo/yr * 30yrs = 360 Months.
Plug the above values in the given Eq and get:
P1 = $434,810.88
I = P1-Po
B. P2 = (Po*r*t)/(1-(1+r)^-t)
Use same procedure as A.
To calculate the interest savings, we need to compare the total interest paid on the current mortgage to the total interest paid on the new mortgage. Here's how you can calculate it step-by-step:
1. Calculate the monthly payment for the current mortgage using the current interest rate and loan details. To do this, you can use a mortgage payment calculator or a spreadsheet software like Excel. The formula to calculate the monthly payment is:
Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
- P = principal loan amount ($225,000)
- r = monthly interest rate (annual rate / 12)
- n = total number of monthly payments (30 years * 12 months)
Substituting the values, we have:
- r = 5% / 12 = 0.004167
- n = 30 years * 12 months = 360 months
Using the formula, you can calculate the monthly payment for the current mortgage.
2. Calculate the total interest paid on the current mortgage over its 30-year term. To do this, multiply the monthly payment by the total number of payments and subtract the principal loan amount. The formula is:
Total interest paid = (Monthly payment * Total number of payments) - Principal loan amount
Substituting the values, you can calculate the total interest paid on the current mortgage.
3. Calculate the monthly payment for the new mortgage using the new interest rate and loan term. Repeat step 1 using the updated interest rate (3.5%) and a loan term of 15 years (or 180 months).
4. Calculate the total interest paid on the new mortgage over its 15-year term using the same formula as step 2.
5. Subtract the total interest paid on the new mortgage from the total interest paid on the current mortgage to determine the interest savings.
So, by following these steps, you can calculate the interest savings if you refinance your loan at 3.5% for 15 years.