In how many years will a sum of money triple itself at 10% per annum compound in
Practice Questions
Q1
In how many years will a sum of money triple itself at 10% per annum compound interest? (2023)
10 years
12 years
15 years
20 years
Questions & Step-by-Step Solutions
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.
