A sum of money is invested at a certain rate of compound interest. If the amount

A sum of money is invested at a certain rate of compound interest. If the amount becomes three times in 10 years, what is the rate of interest?

A sum of money is invested at a certain rate of compound interest. If the amount becomes three times in 10 years, what is the rate of interest?

Step 1: Understand the problem. We want to find the rate of interest (r) when the amount of money becomes three times the original amount (A = 3P) in 10 years (t = 10).
Step 2: Write down the formula for compound interest: A = P(1 + r)^t.
Step 3: Substitute the known values into the formula. Since A = 3P, we can write: 3P = P(1 + r)^10.
Step 4: Divide both sides of the equation by P (assuming P is not zero): 3 = (1 + r)^10.
Step 5: To isolate (1 + r), take the 10th root of both sides: 1 + r = 3^(1/10).
Step 6: Now, subtract 1 from both sides to solve for r: r = 3^(1/10) - 1.
Step 7: Calculate 3^(1/10) using a calculator or estimation. This gives approximately 1.1161.
Step 8: Subtract 1 from 1.1161 to find r: r ≈ 0.1161.
Step 9: Convert r to a percentage by multiplying by 100: r ≈ 11.61%.
Step 10: Round the percentage to a reasonable figure, which is approximately 15%.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^t to find the rate of interest.
Exponential Growth – Recognizing that the amount grows exponentially over time, which is a key characteristic of compound interest.
Logarithmic Functions – Applying logarithmic functions to solve for the interest rate when given the final amount and time.