A sum of money doubles itself in 5 years at simple interest. How long will it ta

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Question: A sum of money doubles itself in 5 years at simple interest. How long will it take to triple itself?

Options:

Correct Answer: 20 years

Solution:

If it doubles in 5 years, the interest rate is 20% per annum. To triple, it needs to earn 200% interest, which will take 10 years.

A sum of money doubles itself in 5 years at simple interest. How long will it take to triple itself?

A sum of money doubles itself in 5 years at simple interest. How long will it take to triple itself?

Step 1: Understand that the money doubles in 5 years at simple interest.
Step 2: Calculate the interest rate. Since the money doubles, the interest earned is equal to the original amount. Therefore, if the original amount is 100, the interest earned in 5 years is also 100.
Step 3: Use the formula for simple interest: Interest = Principal × Rate × Time. Here, Interest = 100, Principal = 100, and Time = 5 years.
Step 4: Rearrange the formula to find the rate: Rate = Interest / (Principal × Time). So, Rate = 100 / (100 × 5) = 0.20 or 20%.
Step 5: To triple the money, the total interest needed is 200% of the original amount (which is 2 times the original amount).
Step 6: Use the same formula for simple interest to find the time needed to earn 200% interest: 200 = 100 × Rate × Time.
Step 7: Substitute the rate (20% or 0.20) into the formula: 200 = 100 × 0.20 × Time.
Step 8: Solve for Time: Time = 200 / (100 × 0.20) = 200 / 20 = 10 years.

Simple Interest Calculation – Understanding how simple interest works and how to calculate the time required for a sum of money to double or triple.
Interest Rate Application – Applying the interest rate derived from the doubling time to determine the time required for tripling the amount.