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

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

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

Correct Answer: 10%

Step 1: Understand that we want to find the rate of interest (r) when a sum of money doubles 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 of interest, 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 of the equation 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 = 0.1487.
Step 8: Convert r into a percentage by multiplying by 100: r = 0.1487 * 100 = 14.87%.
Step 9: Round the answer to a reasonable percentage, which is approximately 15%.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^n to calculate the rate of interest.
Exponential Growth – Recognizing that the doubling of an amount in a fixed time period indicates exponential growth, which is a key characteristic of compound interest.