The Sandersons are planning to refinance their home. The outstanding principal on their original loan is $110,000 and was to amortized in 240 equal monthly installments at an interest rate of 11%/year compounded monthly. The new loan they expect to secure is to be amortized over the same period at an interest rate of 8%/year compounded monthly. How much less can they expect to pay over the life of the loan in interest payments by refinancing the loan at this time? (Round your answer to the nearest cent.)

Question

The Sandersons are planning to refinance their home. The outstanding principal on their original loan is $110,000 and was to amortized in 240 equal monthly installments at an interest rate of 11%/year compounded monthly. The new loan they expect to secure is to be amortized over the same period at an interest rate of 8%/year compounded monthly. How much less can they expect to pay over the life of the loan in interest payments by refinancing the loan at this time? (Round your answer to the nearest cent.)

Answer 1

To find out how much less the Sandersons can expect to pay over the life of the loan in interest payments by refinancing, we need to calculate the total interest paid for both the original loan and the new loan.

For the original loan, we can use the formula for the monthly payment on an amortizing loan:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:
P = Monthly Payment
r = Monthly interest rate
PV = Present value (loan amount)
n = Number of monthly payments

Let's calculate the monthly payment for the original loan:

PV = $110,000
r = Annual interest rate / 12 (since it is compounded monthly) = 11% / 12 = 0.9167%
n = 240

Using these values in the formula, we can find the monthly payment for the original loan:

P = (0.9167% * $110,000) / (1 - (1 + 0.9167%)^(-240))
P ≈ $1,169.92

Now, let's calculate the total interest paid for the original loan:

Total Interest Paid = (Monthly Payment * Number of Payments) - Present Value
Total Interest Paid = ($1,169.92 * 240) - $110,000
Total Interest Paid ≈ $65,177.81

Now, let's calculate the monthly payment for the new loan:

PV remains the same since they are refinancing the original loan.

r = 8% / 12 = 0.6667%
n remains the same at 240.

Using these values in the formula, we can find the monthly payment for the new loan:

P = (0.6667% * $110,000) / (1 - (1 + 0.6667%)^(-240))
P ≈ $979.73

Now, let's calculate the total interest paid for the new loan:

Total Interest Paid = ($979.73 * 240) - $110,000
Total Interest Paid ≈ $50,033.45

Finally, let's calculate how much less the Sandersons can expect to pay over the life of the loan:

Interest Savings = Total Interest Paid (Original Loan) - Total Interest Paid (New Loan)
Interest Savings = $65,177.81 - $50,033.45
Interest Savings ≈ $15,144.36

Therefore, the Sandersons can expect to pay approximately $15,144.36 less in interest payments by refinancing the loan at this time.