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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 annual interest rate?

Options:

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

Correct Answer: 15%

Solution: 

Using the formula A = P(1 + r)^n, we have 3P = P(1 + r)^10. Thus, (1 + r)^10 = 3. Solving gives r ≈ 0.15 or 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 annual interest rate?
  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 annual interest rate?
  • Step 1: Understand that we are using the formula for compound interest, which is A = P(1 + r)^n.
  • Step 2: Identify what each symbol means: A is the final amount, P is the initial amount (principal), r is the annual interest rate, and n is the number of years.
  • Step 3: In this problem, we know that the amount becomes three times the initial amount after 10 years. So we can write A as 3P.
  • Step 4: Substitute A in the formula: 3P = P(1 + r)^10.
  • Step 5: Divide both sides of the equation by P (assuming P is not zero): 3 = (1 + r)^10.
  • Step 6: To find r, we need to isolate it. Take the 10th root of both sides: 1 + r = 3^(1/10).
  • Step 7: Calculate 3^(1/10) using a calculator or estimation. This gives approximately 1.116.
  • Step 8: Now, subtract 1 from both sides to find r: r = 1.116 - 1.
  • Step 9: This simplifies to r ≈ 0.116, which is about 0.15 when rounded.
  • Step 10: Convert r to a percentage by multiplying by 100: r ≈ 15%.
  • Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^n to calculate the future value of an investment.
  • Exponential Growth – Recognizing that the relationship between time and growth in compound interest is exponential, which can lead to non-linear results.
  • Algebraic Manipulation – Ability to manipulate equations to isolate variables and solve for the interest rate.
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