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?

Question

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First, we need to calculate the original monthly mortgage payment. We can use the PMT function in Excel or a financial calculator to find this value. Using the information given, we get:

PMT = -$926.23

(We use a negative sign because this represents a payment.)

Next, we need to calculate the new monthly mortgage payment with the additional $50 payment. This can also be done using the PMT function. Since the payment is increasing, the present value (PV) of the loan will be decreasing with each payment. Therefore, we need to use the original loan amount minus the payments that have already been made as the present value. This gives us:

PMT = -$976.23

So the additional $50 payment increases the monthly payment by $50.

Now we can calculate the interest savings by pre-paying. We can do this by comparing the total interest paid for the original mortgage with the total interest paid for the mortgage with the $50 pre-payment. Again, we can use Excel or a financial calculator to do this.

For the original mortgage:

Total interest = -$155,000 x 6% x 25 years = -$139,500

For the new mortgage with the $50 payment:

Total interest = -$155,000 x 6% x 25 years - ($50 x 12 x 25) = -$122,347.78

(Note that we are subtracting the total additional payments made over the life of the loan.)

So the interest savings is:

Interest savings = -$139,500 - (-$122,347.78) = -$17,152.22

Therefore, the answer is:

Answer: C

Your Current $155,000 Mortgage Calls for Monthly Payments Over 25