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 20 year mortgage at 4.2% 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
Your original payment is correct, I got the same.
Amount owing after 10 years
= 202916.70(1.00725)^120 - 1589.11(1.00725^120 - 1)/.00725
= 180472.95 YEAHH, you had that
new plan: 20 years at .042
i = .042/12 = .0035
WHY ARE YOU TALKING ABOUT A 15 YR MORTGAGE?
Should be 20 years
180472.95 = p (1 - 1.0035^-240)/.0035
p = 1112.74
Think I found your error, take it from here.
SHOOT THE ORIFINAL QUESTION IS TO COMPARE A 15 YEAR MORTGAGE AT 5.1% NOT THE 20 YR AT 4.2%. PLEASE TAKE ANOTHER LOOK IF YOU CAN:)
Ok , I found the new monthly payment for the 15 year, at 5.1% and also got 1436.59
The interest on the original plan would have been
360(1589.11) - 202916.70 = 369161.35
which you got
interest with new plan
= 120(1589.11) + 180(1436.59) - 202916.70
= 190692.68 + 258586.20 - 202916.70
= 246362.18
difference in interest paid
= 369161.35 - 246362.18
= 122799.17
mmmhhh?
so your getting the same thing? huh
yup!
To find the correct answer, let's break down the steps and calculations one by one:
Step 1: Calculate the original mortgage details
- The original home price was $225,463.
- The down payment was 10% of the home price, which is $225,463 * 0.1 = $22,546.30.
- The loan amount is the remaining balance, which is $225,463 - $22,546.30 = $202,916.70.
- The original mortgage term is 30 years, or 360 months.
- The interest rate is 8.7% compounded monthly.
To calculate the monthly payment on the original mortgage, you can use the formula for a monthly mortgage payment:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments))
Where:
- Loan Amount = $202,916.70
- Monthly Interest Rate = Annual Interest Rate / 12 months = 8.7% / 12 = 0.725%
- Total Number of Payments = Mortgage Term in years * 12 = 30 * 12 = 360
Plugging in the values:
Monthly Payment = ($202,916.70 * 0.00725) / (1 - (1 + 0.00725)^(-360))
Monthly Payment = $1,583.40
So, the monthly payment on the original mortgage is $1,583.40.
Step 2: Calculate the total interest paid on the original 30-year mortgage
- To find the total interest paid over the 30-year term, multiply the monthly payment by the total number of payments and subtract the original loan amount.
- Total Interest Paid = (Monthly Payment * Total Number of Payments) - Loan Amount
- Total Interest Paid = ($1,583.40 * 360) - $202,916.70
- Total Interest Paid = $569,307.51 - $202,916.70
- Total Interest Paid = $366,390.81
So, the total interest paid on the original 30-year mortgage is $366,390.81.
Step 3: Calculate the unpaid balance after 10 years
- To find the unpaid balance, we need to determine the remaining loan amount after 10 years.
- The number of payments made in 10 years would be 10 * 12 = 120.
- To calculate the unpaid balance, we need to use the formula for the remaining loan balance on a mortgage:
Remaining Loan Balance = Loan Amount * (1 + Monthly Interest Rate)^(Total Number of Payments) - (Monthly Payment * (((1 + Monthly Interest Rate)^(Total Number of Payments)) - 1) / Monthly Interest Rate))
Where:
- Loan Amount = $202,916.70
- Monthly Interest Rate = 8.7% / 12 = 0.725%
- Total Number of Payments = 360
- Monthly Payment = $1,583.40
Plugging in the values:
Remaining Loan Balance = $202,916.70 * (1 + 0.00725)^(360) - ($1,583.40 * (((1 + 0.00725)^(360)) - 1) / 0.00725)
Remaining Loan Balance = $180,953.20
So, the unpaid balance after 10 years is $180,953.20.
Step 4: Calculate the new mortgage details
- The new mortgage term is 20 years, or 240 months.
- The interest rate is 4.2% compounded monthly.
To calculate the monthly payment for the new mortgage, use the same formula as before:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments))
Where:
- Loan Amount = Remaining Loan Balance on the original mortgage = $180,953.20
- Monthly Interest Rate = Annual Interest Rate / 12 months = 4.2% / 12 = 0.35%
- Total Number of Payments = Mortgage Term in years * 12 = 20 * 12 = 240
Plugging in the values:
Monthly Payment = ($180,953.20 * 0.0035) / (1 - (1 + 0.0035)^(-240))
Monthly Payment = $1,436.19
So, the monthly payment on the new mortgage is $1,436.19.
Step 5: Calculate the total interest paid on the new 20-year mortgage
- To find the total interest paid over the 20-year term, multiply the monthly payment by the total number of payments and subtract the remaining loan balance.
- Total Interest Paid = (Monthly Payment * Total Number of Payments) - Remaining Loan Balance
- Total Interest Paid = ($1,436.19 * 240) - $180,953.20
- Total Interest Paid = $345,884.32 - $180,953.20
- Total Interest Paid = $164,931.12
So, the total interest paid on the new 20-year mortgage is $164,931.12.
Step 6: Calculate the interest savings
- To calculate the interest savings, subtract the total interest paid on the new mortgage from the total interest paid on the original mortgage.
- Interest Savings = Total Interest Paid on Original Mortgage - Total Interest Paid on New Mortgage
- Interest Savings = $366,390.81 - $164,931.12
- Interest Savings = $201,459.69
Therefore, the interest savings from refinancing would be $201,459.69.
Please check if any calculation mistakes were made, and let me know if you have any further questions or need additional clarification.