Calculating Time to Triple the Money at 8% P.a CI

To calculate the time by which a sum of money would treble itself at 8% P.a CI, we need to use the formula for Compound Interest (CI) and solve for time (t).

The formula for CI is:

A = P x (1 + r/100)^t

Where,
A = Final amount
P = Principal amount
r = Rate of interest
t = Time in years

To calculate the time required for the principal amount to triple itself, we can set A = 3P in the above formula.

3P = P x (1 + 8/100)^t

Simplifying the above equation, we get:

(1 + 8/100)^t = 3

Taking log to the base 10 on both sides, we get:

t x log(1.08) = log(3)

t = log(3) / log(1.08)

t = 14.4 years (approx.)

Therefore, the time required for a sum of money to treble itself at 8% P.a CI is approximately 14.4 years.

Explanation

Compound interest is the interest calculated on the principal amount and the accumulated interest over a period of time. In other words, it is the interest earned on the interest.

To calculate the time required for the principal amount to triple itself, we use the formula for CI and equate the final amount (A) to 3 times the principal amount (P). We then solve for time (t) using logarithms.

In this case, the rate of interest (r) is 8% per annum. We convert this to a decimal by dividing by 100.

Once we have the value of t, we can convert it to years, months, or any other unit of time depending on the requirement.

It is important to note that the formula for CI assumes that the interest is compounded annually. If the interest is compounded more frequently, such as half-yearly or quarterly, the formula would need to be modified accordingly.