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Answer :
To solve this problem, let's break it down step by step:
1. Understand the problem:
- You have a loan of [tex]$8,000.
- You need to pay back a total of $[/tex]8,160 after 2 years.
- The interest is simple, meaning the interest is calculated only on the original loan amount.
2. Calculate the total interest paid:
- Subtract the original loan amount from the total amount paid back to find the total interest.
- Total interest = [tex]$8,160 - $[/tex]8,000 = [tex]$160
3. Determine the interest rate:
- Since the interest is simple, use the formula for simple interest:
\[
\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]
- We know the interest ($[/tex]160), the principal ($8,000), and the time (2 years). So we can rearrange the formula to find the interest rate:
[tex]\[
\text{Rate} = \frac{\text{Simple Interest}}{\text{Principal} \times \text{Time}}
\][/tex]
- Substitute the known values:
[tex]\[
\text{Rate} = \frac{160}{8000 \times 2} = 0.01
\][/tex]
4. Identify the correct function:
- Now that we know the interest rate is 0.01, we can write the function for the interest after [tex]\( t \)[/tex] years using the formula:
[tex]\[
f(t) = \text{Principal} \times \text{Rate} \times t
\][/tex]
- Substitute the known values [tex]\( f(t) = 8000 \times 0.01 \times t \)[/tex].
So, the correct function that represents the interest on this loan after [tex]\( t \)[/tex] years is:
[tex]\[
f(t) = 8000 \cdot 0.01 \cdot t
\][/tex]
1. Understand the problem:
- You have a loan of [tex]$8,000.
- You need to pay back a total of $[/tex]8,160 after 2 years.
- The interest is simple, meaning the interest is calculated only on the original loan amount.
2. Calculate the total interest paid:
- Subtract the original loan amount from the total amount paid back to find the total interest.
- Total interest = [tex]$8,160 - $[/tex]8,000 = [tex]$160
3. Determine the interest rate:
- Since the interest is simple, use the formula for simple interest:
\[
\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]
- We know the interest ($[/tex]160), the principal ($8,000), and the time (2 years). So we can rearrange the formula to find the interest rate:
[tex]\[
\text{Rate} = \frac{\text{Simple Interest}}{\text{Principal} \times \text{Time}}
\][/tex]
- Substitute the known values:
[tex]\[
\text{Rate} = \frac{160}{8000 \times 2} = 0.01
\][/tex]
4. Identify the correct function:
- Now that we know the interest rate is 0.01, we can write the function for the interest after [tex]\( t \)[/tex] years using the formula:
[tex]\[
f(t) = \text{Principal} \times \text{Rate} \times t
\][/tex]
- Substitute the known values [tex]\( f(t) = 8000 \times 0.01 \times t \)[/tex].
So, the correct function that represents the interest on this loan after [tex]\( t \)[/tex] years is:
[tex]\[
f(t) = 8000 \cdot 0.01 \cdot t
\][/tex]
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