If a sum of money doubles in 5 years at compound interest, what is the rate of i

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Question: If a sum of money doubles in 5 years at compound interest, what is the rate of interest?

Options:

Correct Answer: 10%

Solution:

Using the formula A = P(1 + r)^t, if A = 2P, then 2 = (1 + r)^5. Solving gives r = 10%.

If a sum of money doubles in 5 years at compound interest, what is the rate of interest?

If a sum of money doubles in 5 years at compound interest, what is the rate of interest?

Step 1: Understand that we are using the compound interest formula A = P(1 + r)^t, where A is the final amount, P is the principal amount (initial sum), r is the rate of interest, and t is the time in years.
Step 2: Since the sum of money doubles in 5 years, we can say A = 2P (the final amount is twice the principal).
Step 3: Substitute A = 2P 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 find r, we need to solve the equation 2 = (1 + r)^5. 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: 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 percentage to a common value, which is approximately 10%.

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 – Ability to manipulate equations to isolate variables and solve for the interest rate.