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The following table shows a portion of a three-year amortization schedule.3-year amortization schedule. Loan amount or principal: 12,240 dollars. Interest rate on loan: 8.71 percent. A 5-column table with 7 rows. Column 1 is labeled Month with entries 13, 14, 15, 16, 17, 18, 19. Column 2 is labeled payment and all entries are 387 dollars and 58 cents. Column 3 is labeled Principal with entries 325.82, 328.19, 330.57, 332.97, 335.38, 337.82, 340.27. Column 4 is labeled Interest with entries 61.76, 59.39, 57.01, 54.61, 52.19, 49.76, 47.31. Column 5 is labeled Balance with entries 8,182.71, 7,854.52, 7,523.95, 7,190.99, 6,855.60, 6,517.78, 6,177.51.Use the information in the table to decide which of the following statements is true.a.The payment amount changes each month.b.The amount applied to the principal is decreasing each month.c.The amount applied to the principal is increasing each month.d.The amount applied to interest is increasing each month.
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Solution Steps
To determine which statement is true, we need to analyze the given amortization schedule. Specifically, we should look at the "Principal" and "Interest" columns to see how the amounts applied to the principal and interest change each month.
- Check if the payment amount changes each month.
- Check if the amount applied to the principal is decreasing each month.
- Check if the amount applied to the principal is increasing each month.
- Check if the amount applied to interest is increasing each month.
Step 1: Check if the payment amount changes each month
The payment amounts are given as:\[ \text{payments} = [387.58, 387.58, 387.58, 387.58, 387.58, 387.58, 387.58] \]
Since all payment amounts are equal, the payment amount does not change each month.
Step 2: Check if the amount applied to the principal is decreasing each month
The principal amounts are given as:\[ \text{principal} = [325.82, 328.19, 330.57, 332.97, 335.38, 337.82, 340.27] \]
We observe that:\[ 325.82 < 328.19 < 330.57 < 332.97 < 335.38 < 337.82 < 340.27 \]
Since each subsequent principal amount is greater than the previous one, the amount applied to the principal is increasing each month.
Step 3: Check if the amount applied to interest is increasing each month
The interest amounts are given as:\[ \text{interest} = [61.76, 59.39, 57.01, 54.61, 52.19, 49.76, 47.31] \]
We observe that:\[ 61.76 > 59.39 > 57.01 > 54.61 > 52.19 > 49.76 > 47.31 \]
Since each subsequent interest amount is less than the previous one, the amount applied to interest is decreasing each month.
Final Answer
Based on the analysis, the correct statement is:\[ \boxed{\text{c. The amount applied to the principal is increasing each month.}} \]
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