A sum of money doubles itself in 5 years at a certain rate of compound interest.

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Question: A sum of money doubles itself in 5 years at a certain rate of compound interest. What is the rate?

Options:

Correct Answer: 14.87%

Solution:

Using the formula A = P(1 + r)^n, if A = 2P, then 2 = (1 + r)^5. Solving gives r ≈ 14.87%.

A sum of money doubles itself in 5 years at a certain rate of compound interest. What is the rate?

A sum of money doubles itself in 5 years at a certain rate of compound interest. What is the rate?

Step 1: Understand that we want to find the rate of interest (r) that makes a sum of money double in 5 years.
Step 2: Use the formula for compound interest, which is A = P(1 + r)^n, where A is the final amount, P is the principal amount, r is the rate, and n is the number of years.
Step 3: Since the money doubles, we can say A = 2P. Substitute this into the formula: 2P = P(1 + r)^5.
Step 4: Divide both sides by P (assuming P is not zero): 2 = (1 + r)^5.
Step 5: To isolate (1 + r), take the fifth root of both sides: (1 + r) = 2^(1/5).
Step 6: Calculate 2^(1/5), which is approximately 1.1487.
Step 7: Now, subtract 1 from both sides to find r: r = 1.1487 - 1.
Step 8: This gives r ≈ 0.1487, or as a percentage, r ≈ 14.87%.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^n.
Exponential Growth – Recognizing that the relationship between time and growth in compound interest is exponential.
Rate Calculation – Calculating the interest rate from the compound interest formula.