Final answer:
a. The amount of the new loan is $56,108. b. The new monthly payment is approximately $462.91. c. The amount saved by refinancing is $348,552.
Step-by-step explanation:
To answer this question, we need to calculate the amount of the new loan, the new monthly payment, and the amount saved by refinancing. Let's solve each part step by step:
- Amount of the new loan (amount refinanced): To find this, we need to subtract the principal amount they have already paid from the original loan amount. The principal amount they have paid can be calculated as the sum of 120 payments made at $1,199.10 each. So, the principal amount paid is $1199.10 x 120 = $143,892. Now, subtracting this from the original loan amount, we get $200,000 - $143,892 = $56,108. Therefore, the amount of the new loan is $56,108.
- New monthly payment: To find this, we can use the formula for the monthly payment of a loan, which is given as: PMT = (P * r) / (1 - (1+r)^(-n)). Here P is the principal loan amount, r is the monthly interest rate, and n is the total number of payments. Substituting the values into the formula, we have: PMT = ($56,108 * (0.045/12)) / (1 - (1 + (0.045/12))^(-15*12)). Calculating this expression, we find that the new monthly payment is approximately $462.91.
- Amount saved by refinancing: To find this, we need to calculate the total cost of the original loan and the total cost of the newly refinanced loan. The total cost of the original loan can be calculated as the sum of 360 monthly payments of $1,199.10. So, the total cost of the original loan is $1,199.10 x 360 = $431,676. The total cost of the new loan can be calculated as the sum of 180 monthly payments of $462.91. So, the total cost of the new loan is $462.91 x 180 = $83,124. Finally, subtracting the total cost of the new loan from the total cost of the original loan, we get the amount saved by refinancing: $431,676 - $83,124 = $348,552. Therefore, the amount saved by refinancing is $348,552.