Question
rylee took out a loan for $3600 at 13% interest, compounded annually. if she makes yearly payments of $460, will she ever pay off the loan?
A. yes, because $460 is less than the amount of interest she is charged per year
B. no, because $460 is less than the amount of interest she is charged per year
C. yes, because $460 is greater than the amount of interest she is charged per year
D. no, because $460 is greater than the amount of interest she is charged per year
A. yes, because $460 is less than the amount of interest she is charged per year
B. no, because $460 is less than the amount of interest she is charged per year
C. yes, because $460 is greater than the amount of interest she is charged per year
D. no, because $460 is greater than the amount of interest she is charged per year
Answers
GPT-4o mini
To determine whether Rylee will pay off the loan with her yearly payments of $460, we need to calculate the amount of interest charged per year on the $3,600 loan at a 13% interest rate.
**Step 1: Calculate the annual interest.**
The annual interest can be calculated using the following formula:
\[
\text{Interest} = \text{Principal} \times \text{Rate}
\]
Substituting the values in:
\[
\text{Interest} = 3600 \times 0.13 = 468
\]
**Step 2: Compare the interest to the yearly payment.**
Rylee makes yearly payments of $460. Since the annual interest is $468, we compare the two:
- Annual Interest: $468
- Yearly Payment: $460
**Conclusion:**
Since the yearly payment of $460 is less than the amount of interest charged per year ($468), Rylee will not be able to cover the interest with her payments. This means that the loan will continue to grow because she is not paying enough to cover even the interest, let alone the principal.
Therefore, the correct answer is:
**B. no, because $460 is less than the amount of interest she is charged per year.**
**Step 1: Calculate the annual interest.**
The annual interest can be calculated using the following formula:
\[
\text{Interest} = \text{Principal} \times \text{Rate}
\]
Substituting the values in:
\[
\text{Interest} = 3600 \times 0.13 = 468
\]
**Step 2: Compare the interest to the yearly payment.**
Rylee makes yearly payments of $460. Since the annual interest is $468, we compare the two:
- Annual Interest: $468
- Yearly Payment: $460
**Conclusion:**
Since the yearly payment of $460 is less than the amount of interest charged per year ($468), Rylee will not be able to cover the interest with her payments. This means that the loan will continue to grow because she is not paying enough to cover even the interest, let alone the principal.
Therefore, the correct answer is:
**B. no, because $460 is less than the amount of interest she is charged per year.**