Calculating the Rate of Interest

To calculate the rate of interest per annum, we need to use the formula for simple interest:

Simple Interest = (Principal * Rate * Time) / 100

Given that the sum triples in 15 years, we can assume that the principal amount is P and the amount after 15 years is 3P. The time is 15 years.

Substituting these values into the formula, we get:

3P = (P * Rate * 15) / 100

Simplifying the Equation

To solve for the rate, we can simplify the equation further:

3P * 100 = P * Rate * 15

300P = 15P * Rate

Rate = (300P) / (15P)

Rate = 20

Interpreting the Result

The rate of interest per annum is 20%. This means that if you invest a sum of money at a simple interest rate of 20% per annum, the amount will triple in 15 years.

Explanation of the Steps

1. We start by using the formula for simple interest: Simple Interest = (Principal * Rate * Time) / 100.
2. Since the sum triples in 15 years, we set the principal amount as P and the amount after 15 years as 3P.
3. Substituting these values into the formula, we get 3P = (P * Rate * 15) / 100.
4. To solve for the rate, we simplify the equation further by multiplying both sides by 100, resulting in 300P = 15P * Rate.
5. We then divide both sides by 15P to isolate the rate, which gives us Rate = (300P) / (15P).
6. Simplifying the expression, we find that the rate is 20.
7. Therefore, the rate of interest per annum is 20%.

Summary

To find the rate of interest per annum when a sum triples in 15 years at a simple rate of interest, we can use the formula for simple interest. By substituting the given values into the formula and simplifying the equation, we find that the rate is 20%. This means that if you invest a sum of money at a simple interest rate of 20% per annum, the amount will triple in 15 years.