To solve for $r$ in the equation $F = P(1 + \frac{r}{100})$, follow these steps:

Step 1: Isolate the term containing $r$

Start by dividing both sides of the equation by $P$ to get rid of $P$ on the right side: $\frac{F}{P} = 1 + \frac{r}{100}$

Step 2: Subtract 1 from both sides

Subtract 1 from both sides to isolate the fraction with $r$: $\frac{F}{P} - 1 = \frac{r}{100}$

Step 3: Multiply both sides by 100

Multiply both sides of the equation by 100 to solve for $r$: $r = 100\left(\frac{F}{P} - 1\right)$

Final Answer

$r = 100 \left(\frac{F - P}{P}\right)$

Let me know if you need more details or have any questions!

Related Questions:

1. How would you solve the equation if it included compounding, such as $F = P(1 + \frac{r}{100})^n$?
2. What is the relationship between $F$, $P$, and $r$ in the context of simple interest?
3. How does the formula $F = P(1 + \frac{r}{100})$ relate to percentage increase calculations?
4. Can you express $r$ in terms of $F$, $P$, and another parameter, say time $t$?
5. What happens to the value of $r$ if $F = 2P$?

Tip:

When solving equations, isolating the variable of interest (in this case, $r$) by systematically undoing operations is key to finding the solution.