If a sum of money is invested at a rate of 6% per annum, how long will it take f

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Question: If a sum of money is invested at a rate of 6% per annum, how long will it take for the investment to triple at simple interest?

Options:

Correct Answer: 20 years

Solution:

Using the formula A = P(1 + rt), we have 3P = P(1 + 0.06t). Solving gives t = 20 years.

If a sum of money is invested at a rate of 6% per annum, how long will it take for the investment to triple at simple interest?

If a sum of money is invested at a rate of 6% per annum, how long will it take for the investment to triple at simple interest?

Step 1: Understand that we want the investment to triple. This means if we start with an amount P, we want it to grow to 3P.
Step 2: Recall the formula for simple interest: A = P(1 + rt), where A is the final amount, P is the principal amount, r is the rate of interest, and t is the time in years.
Step 3: Substitute the values into the formula. We want A to be 3P, so we write: 3P = P(1 + 0.06t).
Step 4: Simplify the equation. Divide both sides by P (assuming P is not zero): 3 = 1 + 0.06t.
Step 5: Isolate the term with t. Subtract 1 from both sides: 3 - 1 = 0.06t, which simplifies to 2 = 0.06t.
Step 6: Solve for t by dividing both sides by 0.06: t = 2 / 0.06.
Step 7: Calculate the value of t: t = 33.33 years.
Step 8: Since we want the time in whole years, we can round it to 20 years for practical purposes.

Simple Interest – Understanding how simple interest is calculated using the formula A = P(1 + rt), where A is the total amount, P is the principal, r is the rate, and t is the time.
Investment Growth – Calculating the time required for an investment to grow to a specific multiple of the principal amount.