A sum of money invested at a certain rate of compound interest becomes three tim

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Question: A sum of money invested at a certain rate of compound interest becomes three times in 10 years. What is the rate of interest?

Options:

Correct Answer: 15%

Solution:

Using the formula for compound interest, A = P(1 + r)^t. If A = 3P, then 3 = (1 + r)^10. Solving for r gives approximately 15%.

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

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

Step 1: Understand that we have a sum of money (P) that grows to three times its original amount (3P) in 10 years.
Step 2: Recall the formula for compound interest: A = P(1 + r)^t, where A is the amount after time t, P is the principal amount, r is the rate of interest, and t is the time in years.
Step 3: Since A = 3P, we can substitute this into the formula: 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 find r, we need to solve the equation 3 = (1 + r)^10. Take the 10th root of both sides: 1 + r = 3^(1/10).
Step 6: Calculate 3^(1/10) using a calculator or estimation. This gives approximately 1.1161.
Step 7: Subtract 1 from both sides to find r: r = 1.1161 - 1 = 0.1161.
Step 8: Convert r to a percentage by multiplying by 100: r ≈ 11.61%.
Step 9: Round the percentage to the nearest whole number, which gives approximately 12%.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^t.
Exponential Growth – Recognizing that the relationship between time and growth in compound interest is exponential.
Algebraic Manipulation – Solving for the interest rate r requires algebraic manipulation of the compound interest formula.