Calculation of Time taken for a sum of money to treble itself at 8% p.a C.I

Compound interest (C.I) is the interest calculated on the initial principal and also on the accumulated interest of the previous periods of a deposit or a loan. In contrast to simple interest, compound interest is more beneficial for depositors over a long-term investment horizon. The question requires the calculation of the time taken for a sum of money to treble itself at 8% p.a C.I.

Formula for Compound Interest:

The formula for calculating the compound interest is:

A = P (1 + R/100)n

Where A is the amount, P is the principal, R is the rate of interest, and n is the number of years.

Calculation:

To calculate the time taken for a sum of money to treble itself at 8% p.a C.I, we need to use the following formula:

Amount = Principal x (1 + Rate/100)n

Let's assume that the principal (P) is Rs. 100.

Amount after n years = Rs. 300 (since we want the principal to treble itself)

Rate of interest (R) = 8%

Substituting these values in the above formula, we get:

300 = 100 x (1 + 8/100)n

3 = (1.08)n

Taking logarithm on both sides, we get:

n log 1.08 = log 3

n = log 3 / log 1.08

n = 26.58 years (approx.)

Therefore, the time taken for a sum of money to treble itself at 8% p.a C.I is approximately 26.58 years.

Conclusion:

The time taken for a sum of money to treble itself at 8% p.a C.I can be calculated by using the formula for compound interest. The above calculation shows that it takes approximately 26.58 years for a sum of money to treble itself at 8% p.a C.I.