In how many years will a sum of money triple itself at a compound interest rate

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

Options:

Correct Answer: 12 years

Solution:

Using the formula A = P(1 + r)^n, we set A = 3P and solve for n, which gives approximately 12 years.

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

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

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 compound interest rate of 10% per year.
Step 2: Identify the formula for compound interest. The formula 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: Set up the equation. Since we want the money to triple, we set A = 3P. So, the equation becomes 3P = P(1 + 0.10)^n.
Step 4: Simplify the equation. Divide both sides by P (assuming P is not zero), which gives us 3 = (1 + 0.10)^n.
Step 5: Rewrite the equation. This simplifies to 3 = (1.10)^n.
Step 6: Solve for n. To find n, we can use logarithms. Take the logarithm of both sides: log(3) = n * log(1.10).
Step 7: Isolate n. So, n = log(3) / log(1.10).
Step 8: Calculate the values. Using a calculator, find log(3) and log(1.10).
Step 9: Divide the two results to find n. This will give you the number of years it takes for the money to triple.
Step 10: Round the answer. The result will be 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 money grows exponentially under compound interest, which is different from simple interest.
Logarithmic Functions – Applying logarithms to solve for the number of years (n) when dealing with exponential equations.