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

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Question: 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?

Options:

  1. 10%
  2. 15%
  3. 20%
  4. 25%

Correct Answer: 15%

Solution: 

Using the formula A = P(1 + r)^t, where A = 3P, t = 10. Solving for r gives r = (3^(1/10)) - 1, which approximates to 15%.

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

Practice Questions

Q1
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?
  1. 10%
  2. 15%
  3. 20%
  4. 25%

Questions & Step-by-Step Solutions

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.
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