12. Your current $155,000 mortgage calls for monthly payments over 25 years at an annual rate interest rate of 6 percent. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

To calculate the interest savings from pre-paying your mortgage, we need to compare the total interest expense with and without the additional $50 monthly payment.

Step 1: Calculate the total interest expense without pre-payment:
First, we need to determine the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = Annual interest rate / 12 = 6% / 12 = 0.5%

Next, calculate the number of monthly payments over 25 years:
Number of months = 25 years * 12 months/year = 300 months

Now, calculate the monthly payment without pre-payment using the formula for the present value of an ordinary annuity:
Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Loan amount = $155,000
r = Monthly interest rate = 0.5% (0.005)
n = Number of months = 300

Monthly payment = $155,000 * 0.005 * (1 + 0.005)^300 / ((1 + 0.005)^300 - 1)

Using a financial calculator or spreadsheet, this calculation yields a monthly payment of approximately $994.37.

Now, calculate the total interest expense without pre-payment:
Total interest expense = (Monthly payment * Number of months) - Loan amount

Total interest expense = ($994.37 * 300) - $155,000

Total interest expense = $298,311 - $155,000

Total interest expense = $143,311

Step 2: Calculate the total interest expense with pre-payment:
To determine the total interest expense with the additional $50 monthly payment, we will use the new monthly payment amount:

New monthly payment = $994.37 + $50 = $1,044.37

Total interest expense with pre-payment = (New monthly payment * Number of months) - Loan amount

Total interest expense with pre-payment = ($1,044.37 * 300) - $155,000

Total interest expense with pre-payment = $313,311 - $155,000

Total interest expense with pre-payment = $158,311

Step 3: Calculate the interest savings from pre-paying:
Interest savings = Total interest expense without pre-payment - Total interest expense with pre-payment

Interest savings = $143,311 - $158,311

Interest savings = -$15,000

Therefore, by paying an additional $50 each month, you save $15,000 in interest expense over the life of the mortgage.

To calculate the interest savings by pre-paying your mortgage, you need to follow these steps:

Step 1: Calculate the monthly interest rate
Since the annual interest rate is 6 percent, you need to divide it by 12 to get the monthly interest rate. Thus, 6 percent divided by 12 equals 0.5 percent. Convert this percentage to decimal form by dividing by 100. So, the monthly interest rate is 0.005.

Step 2: Calculate the monthly mortgage payment without pre-payment
To calculate the monthly mortgage payment, you can use the standard formula for a fixed-rate mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ],

Where:
M = monthly payment
P = principal (loan amount)
i = monthly interest rate
n = total number of payments

Given:
P = $155,000
i = 0.005 (monthly interest rate)
n = 25 years * 12 months/year = 300 (total number of payments)

Using the above formula, we can calculate the monthly mortgage payment without pre-payment.

Step 3: Calculate the monthly mortgage payment with pre-payment
To calculate the monthly mortgage payment with pre-payment, you need to add the additional $50 to the monthly payment calculated in step 2.

Step 4: Calculate the interest expense without pre-payment
Multiply the monthly mortgage payment without pre-payment by the total number of payments (300 months) to calculate the total interest expense.

Step 5: Calculate the interest expense with pre-payment
Multiply the monthly mortgage payment with pre-payment by the total number of payments (300 months) to calculate the total interest expense.

Step 6: Calculate the interest savings
Subtract the interest expense with pre-payment from the interest expense without pre-payment to find the interest savings.

By following these steps, you can calculate the exact amount of interest expense saved by pre-paying your mortgage.