In how many years will a sum of money triple itself at 10% per annum compound in

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Question: In how many years will a sum of money triple itself at 10% per annum compound interest? (2023)

Options:

Correct Answer: 12 years

Exam Year: 2023

Solution:

Using the formula A = P(1 + r)^n, we set 3P = P(1 + 0.1)^n. Solving gives n ≈ 12 years.

In how many years will a sum of money triple itself at 10% per annum compound interest? (2023)

In how many years will a sum of money triple itself at 10% per annum compound interest? (2023)

Step 1: Understand the problem. We want to find out how many years it will take for a sum of money to triple at a 10% interest rate compounded annually.
Step 2: Identify the formula for compound interest, which is A = P(1 + r)^n, where A is the final amount, P is the principal amount (initial money), r is the interest rate, and n is the number of years.
Step 3: Since we want the money to triple, we can say A = 3P (three times the principal).
Step 4: Substitute A into the formula: 3P = P(1 + 0.1)^n. Here, r = 0.1 because 10% is the same as 0.1 in decimal form.
Step 5: Simplify the equation by dividing both sides by P (assuming P is not zero): 3 = (1 + 0.1)^n.
Step 6: This simplifies to 3 = (1.1)^n.
Step 7: To solve for n, we can take the logarithm of both sides: log(3) = n * log(1.1).
Step 8: Rearrange the equation to find n: n = log(3) / log(1.1).
Step 9: Use a calculator to find log(3) and log(1.1). Calculate n using these values.
Step 10: The result will give you n, which is approximately 12 years.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^n to calculate the time required for an investment to grow.
Exponential Growth – Recognizing that the growth of money in compound interest is exponential, which affects the time it takes to reach a certain amount.