Ron starts with a $100,000 mortgage at 8% for 30 years, annual payments. Ten year into the mortgage Ron is able to refinance the balance of the mortgage at 6%.
a) If he chooses to refinance for 20 years what would his new payments be?
To calculate Ron's new mortgage payments after refinancing at a lower interest rate, we need to know the remaining balance on the mortgage.
Since Ron started with a $100,000 mortgage and made annual payments for ten years, we can calculate the remaining balance using the amortization formula for a mortgage. Let's break down the steps to find the remaining balance:
Step 1: Calculate the number of remaining payments on the original mortgage.
Since the mortgage term is 30 years, and Ron has already made ten years of payments, there are 30 - 10 = 20 years left on the original mortgage.
Step 2: Calculate the remaining balance using the amortization formula.
The amortization formula to calculate the remaining balance on a mortgage is:
M = P * (1 + r)^n - (A/r) * [(1 + r)^n - 1]
Where:
M = Remaining balance
P = Initial mortgage amount ($100,000 in this case)
r = Annual interest rate (8% in this case)
n = Number of remaining payments (20 years in this case)
A = Annual payment amount (unknown)
We can rearrange the formula to solve for A:
A = (r * M) / [(1 + r)^n - 1]
Step 3: Plug in the values into the formula to find the remaining balance.
Using the values we have:
M = Remaining balance (unknown)
P = $100,000
r = 0.08 (8% as a decimal)
n = 20
A = (0.08 * M) / [(1 + 0.08)^20 - 1]
Next, we can calculate the new mortgage payment amount after refinancing at 6% for 20 years. To do this, we use the same formula, just with the new interest rate:
A = (r * M) / [(1 + r)^n - 1]
Using the following values for the refinanced mortgage:
r = 0.06 (6% as a decimal)
n = 20
We can now calculate the new payment amount.
Please note that without knowing the remaining balance, we cannot provide an exact payment amount.