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.)
To calculate how much less the Sandersons can expect to pay over the life of the loan in interest payments by refinancing, we need to compare the total interest paid on the original loan with the total interest paid on the new loan.
Let's break down the problem step by step:
Step 1: Calculate the total interest paid on the original loan.
To calculate the total interest paid on the original loan, we need to use the formula for the monthly payment on an amortizing loan:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P is the monthly payment
A is the loan amount
r is the monthly interest rate
n is the number of monthly installments
For the original loan:
Loan amount (A) = $110,000
Number of monthly installments (n) = 240
Monthly interest rate (r) = 11% / 12 = 0.11 / 12 = 0.00917
Using the formula, we can calculate the monthly payment (P) on the original loan.
Step 2: Calculate the total interest paid on the new loan.
Using similar steps as above, but with the new interest rate, we can calculate the monthly payment on the new loan.
For the new loan:
Loan amount (A) = $110,000
Number of monthly installments (n) = 240
Monthly interest rate (r) = 8% / 12 = 0.08 / 12 = 0.00667
Calculate the monthly payment (P) on the new loan.
Step 3: Calculate the total amount of interest paid on each loan.
To calculate the total interest paid on each loan, we can use the formula:
Total Interest Paid = (P * n) - A
For the original loan, calculate the total interest paid.
For the new loan, calculate the total interest paid.
Step 4: Calculate the difference in total interest paid.
To find out how much less the Sandersons can expect to pay over the life of the loan in interest payments by refinancing, calculate the difference between the total interest paid on the original loan and the total interest paid on the new loan.
Difference = Total Interest Paid (original loan) - Total Interest Paid (new loan)
Round your answer to the nearest cent.
Follow these steps to calculate the answer to the question.