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01 Apr 2025, 21:52
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Option B: \(100r^2 + 10,100r\)
Difference: \(100r\)
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Difficulty:
55%
(hard)
Question Stats:
65% (02:56) correct
35%
(03:01)
wrong
based on 365
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There are two options for the terms of a loan of $10,000r, both of which require repayment of the principal and all associated interest after one year.
Select the expression that represents the total payment due at the end of the year under Option B and the expression that represents the positive Difference between the total payments due under the two options. Make only two selections, one in each column.
- Option A has a simple annual interest rate of r%.
- Option B has a simple annual interest rate of (r + 1)%.
Select the expression that represents the total payment due at the end of the year under Option B and the expression that represents the positive Difference between the total payments due under the two options. Make only two selections, one in each column.
| Option B | Difference | |
| \(10,000r\) | ||
| \(\frac{r+101}{100}\) | ||
| \(100(r + 100)r\) | ||
| \(0.01r + 1\) | ||
| \(100r^2 + 10,100r\) | ||
| \(100r\) |
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Official Answer
Option B: \(100r^2 + 10,100r\)
Difference: \(100r\)
04 Apr 2025, 12:00
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1. The question is essentially asking us to find the total payment due, after one year, under each option.
2. Option A. With an interest rate of r%, the total value will be \(10000r * (100\% + r\%) = 10000r + 100r^2\).
3. Option B. With an interest rate of (r + 1)%, the total value will be \(10000r * (100\% + (r + 1)\%) = 10000r + 100r^2 + 100r = 10100r + 100r^2\).
4. The positive difference between the two options is \(Option \ B - Option \ A = (10100r + 100r^2) - (10000r + 100r^2) = 100r\).
5. Our answer will be: Option B - \(100r^2 + 10100r\) and Difference - \(100r\).
2. Option A. With an interest rate of r%, the total value will be \(10000r * (100\% + r\%) = 10000r + 100r^2\).
3. Option B. With an interest rate of (r + 1)%, the total value will be \(10000r * (100\% + (r + 1)\%) = 10000r + 100r^2 + 100r = 10100r + 100r^2\).
4. The positive difference between the two options is \(Option \ B - Option \ A = (10100r + 100r^2) - (10000r + 100r^2) = 100r\).
5. Our answer will be: Option B - \(100r^2 + 10100r\) and Difference - \(100r\).
