A 30 year fixed rate $100,000 mortgage loan . The interest rate is 7.5% compounded monthly.After 20 years the bank is making an offer to refinance at a lower rate of 4.5% . The estimated closing costs are $3,000?
To calculate the answer, we need to determine the monthly mortgage payments for the initial 30-year period at 7.5% interest rate, and then calculate the remaining balance after 20 years. After that, we can calculate the new monthly mortgage payments for the remaining 10-year period at the reduced interest rate of 4.5%. Finally, we'll add the closing costs to find the total cost of the loan.
Now, let's break down the steps to get the answer:
Step 1: Calculate the monthly mortgage payments for the initial 30-year period at 7.5% interest rate.
First, we need to calculate the monthly interest rate. We can find it by dividing the annual interest rate by 12 (to convert it to monthly):
Monthly interest rate = 7.5% / 12 = 0.625% or 0.00625 (decimal form)
Next, let's calculate the total number of monthly payments for the initial 30-year period:
Total number of monthly payments = 30 years * 12 months per year = 360 months
Now, we can calculate the monthly mortgage payments using the following formula:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly mortgage payment
P = Loan amount ($100,000 in this case)
r = Monthly interest rate (0.00625)
n = Total number of monthly payments (360 months)
By plugging in these values, we can calculate the monthly mortgage payments for the initial 30-year period.
Step 2: Calculate the remaining balance after 20 years.
After 20 years, there will be 240 monthly payments remaining. To calculate the remaining balance, we need to know the current interest rate and the original loan amount.
Step 3: Calculate the new monthly mortgage payments for the remaining 10-year period at a 4.5% interest rate.
We'll use a similar formula as in Step 1, but this time we'll use the new interest rate (4.5%) and the remaining balance calculated in Step 2.
Step 4: Add the closing costs ($3,000) to find the total cost of the loan.
By adding the closing costs to the total of all mortgage payments made throughout the loan period, we can find the total cost.
By following these steps, we can find the answer to the question.