To find the interest rate for a principal of \[tex]$6133 charged \$[/tex]46500 in interest over 10 years, we can follow these steps:
### Given:
- Principal, [tex]\( P = \$6133 \)[/tex]
- Interest, [tex]\( I = \$46500 \)[/tex]
- Time, [tex]\( T = 10 \)[/tex] years
### Step-by-Step Solution:
1. Calculate the interest per year:
We need to first calculate the total interest accrued per year, which is given by dividing the total interest by the number of years:
[tex]\[
\text{Interest per year} = \frac{I}{T} = \frac{\$46500}{10}
\][/tex]
[tex]\[
\text{Interest per year} = \$4650
\][/tex]
2. Calculate the annual interest rate:
To find the interest rate, use the formula:
[tex]\[
\text{Interest rate} = \left(\frac{\text{Interest per year}}{P}\right) \times 100
\][/tex]
Substitute the values:
[tex]\[
\text{Interest rate} = \left(\frac{\$4650}{\$6133}\right) \times 100
\][/tex]
3. Perform the division:
Now, let's divide \[tex]$4650 by \$[/tex]6133:
[tex]\[
\frac{\$4650}{\$6133} \approx 0.758
\][/tex]
4. Convert to percentage:
Multiply the result by 100 to convert it to a percentage:
[tex]\[
0.758 \times 100 = 75.8\%
\][/tex]
So, the interest rate is:
[tex]\[
\boxed{75.8\%}
\][/tex]
This is the rounded answer to 1 decimal place.
