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Answer :
To solve the problem, let's follow the steps needed to understand how the extra payment affects the mortgage:
1. Determine the Original Monthly Payment:
- Imagine you have a 15-year mortgage with a monthly payment (from step 1), for example, [tex]$854.17 before adding any extra payments.
2. Calculate the New Monthly Payment:
- By adding an extra $[/tex]100 to the original payment, the new monthly payment becomes [tex]$954.17.
3. Determine the Number of Payments with the New Payment:
- With the extra payment, the total number of payments needed is reduced to 151 months.
4. Calculate How Much Faster the Loan is Paid Off:
- Originally, the mortgage was set for 180 months (15 years).
- With the extra $[/tex]100 payment each month, the mortgage will be paid off in 151 months.
- You will pay off the loan 29 months faster (180 - 151 = 29 months).
5. Convert How Much Faster to Years:
- To find out how much faster it is in years:
- 29 months is approximately 2.42 years (29 ÷ 12 = 2.4167).
6. Calculate Interest Savings:
- First, calculate the total interest you would pay without the extra payments.
- Then, calculate the total interest with the extra [tex]$100 payment each month.
- The difference in these two interest amounts shows you the interest saved.
- By making the extra $[/tex]100 payments, you save [tex]$9,670.93 in interest.
In conclusion, by adding $[/tex]100 to your monthly mortgage payment, you will pay off your mortgage in 151 months instead of 180, saving about 2.42 years and $9,670.93 in interest payments over the life of the loan.
1. Determine the Original Monthly Payment:
- Imagine you have a 15-year mortgage with a monthly payment (from step 1), for example, [tex]$854.17 before adding any extra payments.
2. Calculate the New Monthly Payment:
- By adding an extra $[/tex]100 to the original payment, the new monthly payment becomes [tex]$954.17.
3. Determine the Number of Payments with the New Payment:
- With the extra payment, the total number of payments needed is reduced to 151 months.
4. Calculate How Much Faster the Loan is Paid Off:
- Originally, the mortgage was set for 180 months (15 years).
- With the extra $[/tex]100 payment each month, the mortgage will be paid off in 151 months.
- You will pay off the loan 29 months faster (180 - 151 = 29 months).
5. Convert How Much Faster to Years:
- To find out how much faster it is in years:
- 29 months is approximately 2.42 years (29 ÷ 12 = 2.4167).
6. Calculate Interest Savings:
- First, calculate the total interest you would pay without the extra payments.
- Then, calculate the total interest with the extra [tex]$100 payment each month.
- The difference in these two interest amounts shows you the interest saved.
- By making the extra $[/tex]100 payments, you save [tex]$9,670.93 in interest.
In conclusion, by adding $[/tex]100 to your monthly mortgage payment, you will pay off your mortgage in 151 months instead of 180, saving about 2.42 years and $9,670.93 in interest payments over the life of the loan.
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