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Answer :
Sure! Let's go through the problem step by step.
We have two investments:
1. A \[tex]$7000 investment.
2. A \$[/tex]5000 investment.
We know the following:
- The interest rate for the \[tex]$7000 investment is 0.6% higher than the interest rate for the \$[/tex]5000 investment.
- The difference in interest earned between the two investments is \[tex]$202.
Let's define the interest rate for the \$[/tex]5000 investment as [tex]\(r\%\)[/tex]. Therefore, the interest rate for the \[tex]$7000 investment will be \((r + 0.6)\%\).
Step-by-step Solution:
1. Convert percentages to decimals for calculation:
- The rate for the \$[/tex]5000 investment: [tex]\(r\%\)[/tex] becomes [tex]\(\frac{r}{100}\)[/tex].
- The rate for the \[tex]$7000 investment: \((r + 0.6)\%\) becomes \(\frac{r + 0.6}{100}\).
2. Calculate the interest for each investment:
- Interest from the \$[/tex]5000 investment:
[tex]\[
\text{Interest} = 5000 \times \frac{r}{100} = 50r
\][/tex]
- Interest from the \[tex]$7000 investment:
\[
\text{Interest} = 7000 \times \frac{r + 0.6}{100} = 70r + 42
\]
3. Set up the equation using the given difference in interest:
\[
70r + 42 - 50r = 202
\]
4. Solve the equation:
\[
20r + 42 = 202
\]
\[
20r = 160
\]
\[
r = \frac{160}{20} = 8.0
\]
So, the interest rate for the \$[/tex]5000 investment is 8%.
5. Calculate the interest rate for the \[tex]$7000 investment:
- Since the \$[/tex]7000 investment rate is 0.6% higher, it would be:
[tex]\[
8 + 0.6 = 8.6\%
\][/tex]
Therefore, the interest rate for the \[tex]$5000 investment is 8%, and the interest rate for the \$[/tex]7000 investment is 8.6%.
We have two investments:
1. A \[tex]$7000 investment.
2. A \$[/tex]5000 investment.
We know the following:
- The interest rate for the \[tex]$7000 investment is 0.6% higher than the interest rate for the \$[/tex]5000 investment.
- The difference in interest earned between the two investments is \[tex]$202.
Let's define the interest rate for the \$[/tex]5000 investment as [tex]\(r\%\)[/tex]. Therefore, the interest rate for the \[tex]$7000 investment will be \((r + 0.6)\%\).
Step-by-step Solution:
1. Convert percentages to decimals for calculation:
- The rate for the \$[/tex]5000 investment: [tex]\(r\%\)[/tex] becomes [tex]\(\frac{r}{100}\)[/tex].
- The rate for the \[tex]$7000 investment: \((r + 0.6)\%\) becomes \(\frac{r + 0.6}{100}\).
2. Calculate the interest for each investment:
- Interest from the \$[/tex]5000 investment:
[tex]\[
\text{Interest} = 5000 \times \frac{r}{100} = 50r
\][/tex]
- Interest from the \[tex]$7000 investment:
\[
\text{Interest} = 7000 \times \frac{r + 0.6}{100} = 70r + 42
\]
3. Set up the equation using the given difference in interest:
\[
70r + 42 - 50r = 202
\]
4. Solve the equation:
\[
20r + 42 = 202
\]
\[
20r = 160
\]
\[
r = \frac{160}{20} = 8.0
\]
So, the interest rate for the \$[/tex]5000 investment is 8%.
5. Calculate the interest rate for the \[tex]$7000 investment:
- Since the \$[/tex]7000 investment rate is 0.6% higher, it would be:
[tex]\[
8 + 0.6 = 8.6\%
\][/tex]
Therefore, the interest rate for the \[tex]$5000 investment is 8%, and the interest rate for the \$[/tex]7000 investment is 8.6%.
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