**Question:**What rate is required to grow 100 to 10,000 in 10 years?**Explanation:**To solve the problem of determining the growth rate required for an investment or value to grow from 100 to 10,000 over a period of 10 years, we can use the formula for compound interest:\[ A = P(1 + r)^n \]Where:- \( A \) is the amount of money accumulated after n years, including interest.- \( P \) is the principal amount (the initial amount of money).- \( r \) is the annual interest rate (decimal).- \( n \) is the number of years.In this scenario:- \( A = 10,000 \)- \( P = 100 \)- \( n = 10 \)We need to find \( r \):1. Substitute the values into the formula:\[ 10,000 = 100(1 + r)^{10} \]2. Divide both sides by 100:\[ 100 = (1 + r)^{10} \]3. Take the 10th root of both sides to solve for \( 1 + r \):\[ (1 + r) = 100^{1/10} \]4. Calculate the 10th root of 100:\[ (1 + r) \approx 1.5849 \]5. Subtract 1 from both sides:\[ r \approx 0.5849 \]6. Convert decimal to percentage:\[ r \approx 58.49\% \]**Conclusion:**The required annual growth rate to grow an amount from 100 to 10,000 in 10 years is approximately 58.49%.

Name: **Question:**What rate is required to grow 100 to 10,000 in 10 years?
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: **Question:**What rate is required to grow 100 to 10,000 in 10 years?**Explanation:**To solve the problem of determining the growth rate required for an investment or value to grow from 100 to 10,000 over a period of 10 years, we can use the formula