Compound Interest Growth Explained

The problem asks us to find the future value of an investment under compound interest. We are given that an initial sum triples in 8 years and need to determine its value after 24 years.

Understanding the Growth Factor

Let the principal amount be P. According to the problem, after t = 8 years, the sum becomes 3P. Using the compound interest formula, let the annual growth factor be (1 + r), where r is the annual interest rate. Assuming interest is compounded annually, the formula is:

Amount = $ P \times (1 + r)^t $

For the first 8 years:

$ 3P = P \times (1 + r)^8 $

Dividing both sides by P, we get the growth factor over 8 years:

$ (1 + r)^8 = 3 $

This means the investment triples every 8 years.

Calculating Amount After 24 Years

We need to find the amount after t = 24 years. The formula is:

$ \text{Amount after 24 years} = P \times (1 + r)^{24} $

We can rewrite (1 + r)^24 using the information from the first 8 years. Since 24 = 8 \times 3, we have:

$ (1 + r)^{24} = (1 + r)^{8 \times 3} = \left((1 + r)^8\right)^3 $

Substitute the value (1 + r)^8 = 3:

$ \left(3\right)^3 = 27 $

So, the growth factor over 24 years is 27.

Now, calculate the final amount using the initial principal P = ₹8000:

$ \text{Amount after 24 years} = ₹8000 \times 27 $

Calculation:

$ ₹8000 \times 27 = ₹216000 $

Final Amount

Therefore, the sum will become ₹216000 after 24 years.