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Sagot :
To determine which statement is true, let's analyze the information provided in the amortization schedule.
### Step-by-Step Analysis:
1. Check if the payment amount changes each month:
- The payment amount listed for months 13 through 19 is $387.58.
- Since it remains constant, statement (a) "The payment amount changes each month." is false.
2. Check if the amount applied to the principal is decreasing each month:
- The principal amounts listed are: [tex]$325.82, $[/tex]328.19, [tex]$330.57, $[/tex]332.97, [tex]$335.38, $[/tex]337.82, $340.27.
- To determine if the principal amount is decreasing, we compare each value with the previous month:
- [tex]$328.19 > $[/tex]325.82
- [tex]$330.57 > $[/tex]328.19
- [tex]$332.97 > $[/tex]330.57
- [tex]$335.38 > $[/tex]332.97
- [tex]$337.82 > $[/tex]335.38
- [tex]$340.27 > $[/tex]337.82
- Since each succeeding principal value is larger than the previous one, the principal amount is not decreasing each month. Thus, statement (b) "The amount applied to the principal is decreasing each month." is false.
3. Check if the amount applied to the principal is increasing each month:
- The principal amounts listed, again, are: [tex]$325.82, $[/tex]328.19, [tex]$330.57, $[/tex]332.97, [tex]$335.38, $[/tex]337.82, $340.27.
- To determine if the principal amount is increasing, every subsequent month should have a higher principal applied amount:
- [tex]$328.19 > $[/tex]325.82
- [tex]$330.57 > $[/tex]328.19
- [tex]$332.97 > $[/tex]330.57
- [tex]$335.38 > $[/tex]332.97
- [tex]$337.82 > $[/tex]335.38
- [tex]$340.27 > $[/tex]337.82
- The values confirm a consistent increase each month. Hence, statement (c) "The amount applied to the principal is increasing each month." is true.
4. Check if the amount applied to interest is increasing each month:
- The interest amounts listed are: [tex]$61.76, $[/tex]59.39, [tex]$57.01, $[/tex]54.61, [tex]$52.19, $[/tex]49.76, $47.31.
- To determine if interest is increasing, we compare each value with the previous month:
- [tex]$59.39 < $[/tex]61.76
- [tex]$57.01 < $[/tex]59.39
- [tex]$54.61 < $[/tex]57.01
- [tex]$52.19 < $[/tex]54.61
- [tex]$49.76 < $[/tex]52.19
- [tex]$47.31 < $[/tex]49.76
- The interest amount is consistently decreasing. Therefore, statement (d) "The amount applied to interest is increasing each month." is false.
### Conclusion:
After analyzing the information from the amortization schedule, the true statement is:
(c) The amount applied to the principal is increasing each month.
### Step-by-Step Analysis:
1. Check if the payment amount changes each month:
- The payment amount listed for months 13 through 19 is $387.58.
- Since it remains constant, statement (a) "The payment amount changes each month." is false.
2. Check if the amount applied to the principal is decreasing each month:
- The principal amounts listed are: [tex]$325.82, $[/tex]328.19, [tex]$330.57, $[/tex]332.97, [tex]$335.38, $[/tex]337.82, $340.27.
- To determine if the principal amount is decreasing, we compare each value with the previous month:
- [tex]$328.19 > $[/tex]325.82
- [tex]$330.57 > $[/tex]328.19
- [tex]$332.97 > $[/tex]330.57
- [tex]$335.38 > $[/tex]332.97
- [tex]$337.82 > $[/tex]335.38
- [tex]$340.27 > $[/tex]337.82
- Since each succeeding principal value is larger than the previous one, the principal amount is not decreasing each month. Thus, statement (b) "The amount applied to the principal is decreasing each month." is false.
3. Check if the amount applied to the principal is increasing each month:
- The principal amounts listed, again, are: [tex]$325.82, $[/tex]328.19, [tex]$330.57, $[/tex]332.97, [tex]$335.38, $[/tex]337.82, $340.27.
- To determine if the principal amount is increasing, every subsequent month should have a higher principal applied amount:
- [tex]$328.19 > $[/tex]325.82
- [tex]$330.57 > $[/tex]328.19
- [tex]$332.97 > $[/tex]330.57
- [tex]$335.38 > $[/tex]332.97
- [tex]$337.82 > $[/tex]335.38
- [tex]$340.27 > $[/tex]337.82
- The values confirm a consistent increase each month. Hence, statement (c) "The amount applied to the principal is increasing each month." is true.
4. Check if the amount applied to interest is increasing each month:
- The interest amounts listed are: [tex]$61.76, $[/tex]59.39, [tex]$57.01, $[/tex]54.61, [tex]$52.19, $[/tex]49.76, $47.31.
- To determine if interest is increasing, we compare each value with the previous month:
- [tex]$59.39 < $[/tex]61.76
- [tex]$57.01 < $[/tex]59.39
- [tex]$54.61 < $[/tex]57.01
- [tex]$52.19 < $[/tex]54.61
- [tex]$49.76 < $[/tex]52.19
- [tex]$47.31 < $[/tex]49.76
- The interest amount is consistently decreasing. Therefore, statement (d) "The amount applied to interest is increasing each month." is false.
### Conclusion:
After analyzing the information from the amortization schedule, the true statement is:
(c) The amount applied to the principal is increasing each month.
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