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Find the interest rate for a principal of [tex]$\$[/tex]6133[tex]$ and charged $[/tex]\[tex]$46500$[/tex] in interest for 10 years.

The formula is:

[tex]\[ \text{Interest Rate} = \left( \frac{I}{P \times T} \right) \times 100 \][/tex]

where:
- [tex]\(I\)[/tex] is the interest charged
- [tex]\(P\)[/tex] is the principal
- [tex]\(T\)[/tex] is the time in years

Steps:
1. Take the interest and divide by the principal.
2. Then divide by the number of years.
3. Multiply by 100.
4. Round your answer to 1 decimal place.

Add your answer:

Sagot :

GinnyAnswer
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.
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