# At what rate of si per annum, a sum triples itself in 40 years?

## At what rate of si per annum, a sum triples itself in 40 years?

To determine the rate of simple interest (SI) per annum at which a sum triples itself in 40 years, we need to find the interest rate that will yield a final amount three times the initial sum over the given time period.

Let's assume the initial sum is 'P' and the interest rate is 'R' per annum.

The formula for calculating the simple interest is:

SI = (P * R * T) / 100,

where: SI is the simple interest, P is the principal sum, R is the rate of interest per annum, and T is the time period in years.

We are given that the sum triples itself, which means the final amount is three times the initial sum:

Final amount = 3 * P.

The time period is 40 years, so T = 40.

Substituting these values into the simple interest formula, we have:

3 * P = (P * R * 40) / 100.

Simplifying the equation:

3 = (R * 40) / 100.

To isolate 'R', we can cross-multiply and solve for 'R':

3 * 100 = R * 40,

300 = 40R.

Dividing both sides by 40:

300/40 = R,

7.5 = R.

Therefore, the rate of simple interest per annum required for a sum to triple itself in 40 years is 7.5%.

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