I screwed up the first post with this question so re posting to find some help.
A person purchased a 225463 home 10 years ago by paying 10% down and sighning a 30 year mortgage at 8.7% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 15 year mortgage at 5.1% compounded monthly. How much interest will refinancing save?
I have been on this for a couple hours and believe I am only off by a fraction and that is why my digital homework is still saying it is correct. Instead of copying 4 pages of home work and math I will post my large findings in hopes someone can see where I messed up.
Monthly payment of original 30yr mortgage = 1589.11
Total interest to be paid on original 30 yr mortgage = 369161.35
Unpaid balance of original loan after 10 years = 180472.95
Total interet paid during 1st ten years on original 30yr mortgage = 168248.93
New monthly payment for 15 yr mortgage = 1436.59
Total interest to be paid on new 15 year mortgage = 78113.25
Total savings:
369161.35-(168248.93+78113.25)=122799.17
And this answer was wrong???? Standing back from the numbers they all look about right using common sense but online homework thing says its wrong? Any help would be much appreciated
check
http://www.jiskha.com/display.cgi?id=1327955169
To calculate the interest saved from refinancing, you need to compare the total interest paid on the original 30-year mortgage with the total interest to be paid on the new 15-year mortgage.
Let's break down the calculation step by step.
1. Calculate the original loan amount: The person purchased a $225,463 home by paying a 10% down payment, so the loan amount is 90% of $225,463, which is $202,916.70.
2. Calculate the monthly interest rate on the original 30-year mortgage: The annual interest rate is 8.7%, so the monthly interest rate will be 8.7% divided by 12, which is 0.725%.
3. Calculate the number of months in 10 years: 10 years multiplied by 12 months per year gives us 120 months.
4. Use the formula for the monthly payment of an amortizing loan to calculate the monthly payment for the original 30-year mortgage:
P = (r * (1 + r)^n) / ((1 + r)^n - 1)
where P is the monthly payment, r is the monthly interest rate, and n is the number of payments.
Plugging in the values:
P = (0.00725 * (1 + 0.00725)^120) / ((1 + 0.00725)^120 - 1)
P ≈ $1,589.11 (rounding to the nearest cent)
5. Calculate the total interest paid on the original 30-year mortgage: Multiply the monthly payment by the total number of payments, and subtract the original loan amount.
Total interest = (P * n) - (loan amount)
Total interest = ($1,589.11 * 120) - $202,916.70
Total interest ≈ $168,248.93 (rounding to the nearest cent)
6. Calculate the unpaid balance of the original loan after 10 years: You can use an amortization calculator or the formula for the remaining balance on an amortizing loan.
Remaining balance = (P * ((1 + r)^n - (1 + r)^t)) / ((1 + r)^n - 1)
where t is the number of payments made.
Plugging in the values:
Remaining balance = ($1,589.11 * ((1 + 0.00725)^120 - (1 + 0.00725)^120)) / ((1 + 0.00725)^120 - 1)
Remaining balance ≈ $180,472.95 (rounding to the nearest cent)
7. Calculate the new monthly interest rate on the 15-year mortgage: The annual interest rate is 5.1%, so the monthly interest rate will be 5.1% divided by 12, which is 0.425%.
8. Calculate the number of months in 15 years: 15 years multiplied by 12 months per year gives us 180 months.
9. Use the formula for the monthly payment of an amortizing loan to calculate the monthly payment for the new 15-year mortgage:
P = (r * (1 + r)^n) / ((1 + r)^n - 1)
Plugging in the values:
P = (0.00425 * (1 + 0.00425)^180) / ((1 + 0.00425)^180 - 1)
P ≈ $1,436.59 (rounding to the nearest cent)
10. Calculate the total interest to be paid on the new 15-year mortgage: Multiply the monthly payment by the total number of payments and subtract the remaining balance on the original loan.
Total interest = (P * n) - (remaining balance)
Total interest = ($1,436.59 * 180) - $180,472.95
Total interest ≈ $78,113.25 (rounding to the nearest cent)
11. Calculate the interest saved from refinancing: Subtract the total interest to be paid on the new 15-year mortgage from the total interest paid on the original 30-year mortgage.
Interest saved = Total interest on original mortgage - Total interest on new mortgage
Interest saved = $168,248.93 - $78,113.25
Interest saved = $90,135.68
So, the correct answer should be approximately $90,135.68 saved in interest by refinancing.