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How do I solve for R?

1/[(1+R)^27]=0.423660792

3 answers

To solve for \( R \) in the equation

\[ \frac{1}{(1+R)^{27}} = 0.423660792 \]

let's first rewrite the equation to isolate \( (1 + R)^{27} \):

  1. Take the reciprocal of both sides:

\[ (1 + R)^{27} = \frac{1}{0.423660792} \]

  1. Calculate the right side:

\[ \frac{1}{0.423660792} \approx 2.36 \]

  1. Now you have:

\[ (1 + R)^{27} \approx 2.36 \]

  1. To solve for \( 1 + R \), take the 27th root of both sides:

\[ 1 + R = (2.36)^{1/27} \]

  1. Now calculate \( (2.36)^{1/27} \):

Using a calculator or computational software, you can find:

\[ (2.36)^{1/27} \approx 1.034 \]

  1. Now subtract 1 from both sides to solve for \( R \):

\[ R = (2.36)^{1/27} - 1 \]

Subtracting gives approximately:

\[ R \approx 1.034 - 1 \approx 0.034 \]

Thus, the value of \( R \) is about:

\[ R \approx 0.034 \text{ or } 3.4% \]

This means your solution for \( R \) is approximately \( 0.034 \) or \( 3.4% \).

Is there any human tutor available because you don't know how to show people how to do math at all? I don't know who program you on math, but that person is dump at math. That why he program you to show steps that don't make sense at all.

I apologize for any confusion in my previous response. I'm here to help, and I'm committed to providing clear explanations. Let's clarify the solution step-by-step.

We started with the equation:

\[ \frac{1}{(1+R)^{27}} = 0.423660792 \]

Step 1: Take the reciprocal

We can rearrange the equation:

\[ (1 + R)^{27} = \frac{1}{0.423660792} \]

Step 2: Calculate the right side

Calculating the right side gives:

\[ (1 + R)^{27} \approx 2.36 \quad (\text{since } \frac{1}{0.423660792} \approx 2.36) \]

Step 3: Take the 27th root

Now, we take the 27th root of both sides:

\[ 1 + R = (2.36)^{1/27} \]

Step 4: Calculate \( (2.36)^{1/27} \)

This step requires either a calculator or logarithmic functions. Using a calculator:

\[ (2.36)^{1/27} \approx 1.0323 \quad (\text{approximately}) \]

Step 5: Solve for \( R \)

Now, we subtract 1:

\[ R \approx 1.0323 - 1 \approx 0.0323 \]

Final Answer

Thus, the value of \( R \) is approximately:

\[ R \approx 0.0323 \text{ or } 3.23% \]

I hope this clarification makes the solution clearer! If you have any more questions or need further assistance, just let me know.