Find the rate of interest. $\newline$ $115.00=100\left(1+\frac{r}{4}\right)^{4 \cdot 1}$

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Q. Find the rate of interest.

\newline

115.00=100\left(1+\frac{r}{4}\right)^{4 \cdot 1}

Simplify exponent: To solve for the interest rate $r$ , we need to isolate $r$ in the equation $115.00 = 100(1 + \frac{r}{4})^{4-1}$ . First, we simplify the exponent on the right side of the equation.
Divide by $100$ : The exponent $4-1$ simplifies to $3$ . So, the equation becomes $115.00 = 100(1 + \frac{r}{4})^3$ .
Take cube root: Next, we divide both sides of the equation by $100$ to isolate the term with $r$ on one side. This gives us $115.00 / 100 = (1 + (r)/4)^3$ .
Subtract $1$ : Performing the division, we get $1.15 = (1 + \frac{r}{4})^3$ .
Isolate $r/4$ : Now, we need to take the cube root of both sides to remove the exponent on the right side. The cube root of $1.15$ is approximately $1.0492$ .
Multiply by $4$ : After taking the cube root, we have $1.0492 \approx 1 + \frac{r}{4}$ .
Convert to percentage: Subtract $1$ from both sides to isolate $(r)/4$ on the right side. This gives us $0.0492 \approx (r)/4$ .
Convert to percentage: Subtract $1$ from both sides to isolate $\frac{r}{4}$ on the right side. This gives us $0.0492 \approx \frac{r}{4}$ .Finally, multiply both sides by $4$ to solve for $r$ . This gives us $r \approx 0.0492 \times 4$ .
Convert to percentage: Subtract $1$ from both sides to isolate $\frac{r}{4}$ on the right side. This gives us $0.0492 \approx \frac{r}{4}$ .Finally, multiply both sides by $4$ to solve for $r$ . This gives us $r \approx 0.0492 \times 4$ .Multiplying $0.0492$ by $4$ gives us $r \approx 0.1968$ .
Convert to percentage: Subtract $1$ from both sides to isolate $\frac{r}{4}$ on the right side. This gives us $0.0492 \approx \frac{r}{4}$ .Finally, multiply both sides by $4$ to solve for $r$ . This gives us $r \approx 0.0492 \times 4$ .Multiplying $0.0492$ by $4$ gives us $r \approx 0.1968$ .To express $r$ as a percentage, we multiply by $\frac{r}{4}$ $0$ . So, $\frac{r}{4}$ $1$ .
Convert to percentage: Subtract $1$ from both sides to isolate $(r)/4$ on the right side. This gives us $0.0492 \approx (r)/4$ .Finally, multiply both sides by $4$ to solve for $r$ . This gives us $r \approx 0.0492 \times 4$ .Multiplying $0.0492$ by $4$ gives us $r \approx 0.1968$ .To express $r$ as a percentage, we multiply by $(r)/4$ $0$ . So, $(r)/4$ $1$ .Multiplying $(r)/4$ $2$ by $(r)/4$ $0$ gives us $(r)/4$ $4$ .