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 payments after refinancing, we need to find the new loan amount based on the remaining balance after 10 years and the new interest rate.
Step 1: Find the remaining balance after 10 years.
To calculate the remaining balance after 10 years, we can use an amortization formula or an online mortgage calculator. However, since the mortgage amount, interest rate, and term are given, we can also use a mortgage loan formula known as the "amortizing loan formula."
The formula to calculate the remaining balance after "n" payments can be written as:
Balance = P * ((1 + r)^n - (1 + r)^p) / ((1 + r)^n - 1)
Where:
- Balance is the remaining balance after "n" payments
- P is the initial loan amount
- r is the interest rate per payment period
- n is the total number of payment periods
- p is the number of payments made
In this case, we have:
P = $100,000
r = 8% per year, or 0.08
n = 30 years
p = 10 years
Using the formula, we can calculate the remaining balance after 10 years:
Balance = 100,000 * ((1 + 0.08)^(30) - (1 + 0.08)^(10)) / ((1 + 0.08)^(30) - 1)
Balance ≈ $58,585.21
So, after 10 years, Ron will have a remaining balance of approximately $58,585.21.
Step 2: Calculate the new loan amount after refinancing.
To calculate the new loan amount, subtract the remaining balance after 10 years from the original loan amount:
New Loan Amount = Initial Loan Amount - Remaining Balance
New Loan Amount = $100,000 - $58,585.21
New Loan Amount ≈ $41,414.79
So, the new loan amount after refinancing will be approximately $41,414.79.
Step 3: Calculate the new payments for a 20-year term at 6% interest rate.
To calculate the new payments, we can use the amortizing loan formula again, but this time with the new loan amount and the new interest rate.
P = $41,414.79
r = 6% per year, or 0.06
n = 20 years
Using the formula, we can calculate the new payments:
Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Payment = 41,414.79 * 0.06 * (1 + 0.06)^(20) / ((1 + 0.06)^(20) - 1)
Payment ≈ $321.05
Therefore, if Ron chooses to refinance for 20 years, his new payments would be approximately $321.05 per year.