A person gets ₹7566 when he invests ₹5000 in compound interest at a rate of “r”  for 15 years find r

We are given that an amount of ₹7566 is obtained after investing ₹5000 at compound interest for 15 years. The rate of interest "r" is unknown, and we need to find it.

The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{100}\right)^t
\]

Where:
- \(A\) is the amount after time \(t\),
- \(P\) is the principal amount,
- \(r\) is the rate of interest (per annum),
- \(t\) is the time in years.

### Given:
- \(A = 7566\),
- \(P = 5000\),
- \(t = 15\),
- \(r\) is the unknown.

Now, substituting the values into the formula:

\[
7566 = 5000 \left(1 + \frac{r}{100}\right)^{15}
\]

Dividing both sides by 5000:

\[
1.5132 = \left(1 + \frac{r}{100}\right)^{15}
\]

Now, we need to solve for \(r\). Taking the 15th root on both sides:

\[
\left(1.5132\right)^{\frac{1}{15}} = 1 + \frac{r}{100}
\]

Calculating the 15th root of 1.5132, and solving for \(r\):It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still solve for the rate manually by following these steps:
1. Divide the final amount by the principal: \(\frac{7566}{5000} = 1.5132\).
2. Take the 15th root of 1.5132: \((1.5132)^{1/15}\).
3. Subtract 1 from the result.
4. Multiply by 100 to get the percentage value of \(r\).

Would you like me to help with another problem or give more details on this one?

Here are 5 related questions to expand this topic:
1. How is the formula for compound interest different from simple interest?
2. What happens if we increase the time period in compound interest calculations?
3. How does the frequency of compounding affect the interest earned?
4. Can you explain how continuous compounding works in finance?
5. What is the difference between nominal and effective interest rates?

**Tip:** In compound interest, even small increases in the interest rate can significantly impact the final amount over long periods.

A person gets ₹7566 when he invests ₹5000 in compound interest at a rate of “r” for 15 years. Find r.

Solve a compound interest problem where ₹5000 is invested for 15 years and grows to ₹7566. Learn how to find the interest rate 'r' using the compound interest formula and exponential growth concepts. Suitable for students in Grades 9-12.

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