rearrange simple interest formula I = prn/100 find P, the principle

To find the principal $ P $ using the simple interest formula $ I = \frac{Prn}{100} $, we can rearrange the formula. Here’s the step-by-step process:

1. Start with the original formula:
\[ I = \frac{Prn}{100} \]

2. Multiply both sides by 100 to get rid of the fraction:
\[ 100I = Prn \]

3. Divide both sides by $ rn $ to solve for $ P $:
\[ P = \frac{100I}{rn} \]

So, the rearranged formula to find the principal $ P $ is:
\[ P = \frac{100I}{rn} \]

Would you like more details or have any questions?

Here are 8 related questions for further practice:

1. If the interest $ I $ is $200, the rate $ r $ is 5%, and the time $ n $ is 2 years, what is the principal $ P $?
2. How does the formula change if interest is compounded annually instead of being simple interest?
3. What would be the new principal if the interest rate doubled, but the interest amount and time period remained the same?
4. How do you derive the formula for the rate $ r $ from the simple interest formula?
5. If the principal $ P $ is $500, the rate $ r $ is 4%, and the time $ n $ is 3 years, what is the interest $ I $?
6. What is the principal $ P $ if the interest $ I $ is $100, the rate $ r $ is 10%, and the time $ n $ is 1 year?
7. If you have a principal of $1000, an interest rate of 6%, and time of 5 years, what will be the interest $ I $?
8. How would the formula change if the time $ n $ is given in months instead of years?

**Tip:** Always keep track of units when dealing with interest problems to avoid errors, especially when converting time periods.

Learn how to rearrange the simple interest formula I = prn/100 to find the principal P. Step-by-step solution provided with examples. Suitable for high school students and anyone interested in financial mathematics.

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