This question asks us to find the annual rate of simple interest at which a sum of money will become three times its original value in a period of 20 years.

Understanding Simple Interest Concepts

Simple interest is calculated only on the initial principal amount. The formula for simple interest is:

\( \text{SI} = \frac{P \times R \times T}{100} \)

Where:

• \( \text{SI} \) is the Simple Interest earned.
• \( P \) is the Principal amount (the initial sum of money).
• \( R \) is the Rate of interest per annum (what we need to find).
• \( T \) is the Time period in years.

The total amount (A) after \( T \) years is the sum of the principal and the simple interest:

\( A = P + \text{SI} \)

Setting up the Problem for Tripling Money

We are given that the sum of money triples in 20 years. Let the initial principal amount be \( P \).

• Initial Principal = \( P \)
• Time \( (T) \) = 20 years
• Final Amount \( (A) \) = 3 times the principal = \( 3P \)

Using the formula for the total amount, \( A = P + \text{SI} \), we can find the simple interest earned:

\( \text{SI} = A - P \)

\( \text{SI} = 3P - P \)

\( \text{SI} = 2P \)

So, the simple interest earned over 20 years is equal to twice the original principal amount.

Calculating the Simple Interest Rate

Now we can use the simple interest formula \( \text{SI} = \frac{P \times R \times T}{100} \) and substitute the values we know:

• \( \text{SI} = 2P \)
• \( P = P \) (The principal)
• \( R = ? \) (The rate we need to find)
• \( T = 20 \) years

Substitute these into the formula:

\( 2P = \frac{P \times R \times 20}{100} \)

We can divide both sides of the equation by \( P \) (assuming \( P \neq 0 \), which is true for an investment):

\( 2 = \frac{R \times 20}{100} \)

Now, simplify the fraction on the right side:

\( 2 = \frac{20R}{100} \)

\( 2 = \frac{R}{5} \)

To solve for \( R \), multiply both sides by 5:

\( 2 \times 5 = R \)

\( R = 10 \)

The rate percent per annum is 10%.

Verification of the Simple Interest Rate

Let's quickly check if a principal \( P \) grows to \( 3P \) in 20 years at 10% simple interest.

\( \text{SI} = \frac{P \times R \times T}{100} \)

\( \text{SI} = \frac{P \times 10 \times 20}{100} \)

\( \text{SI} = \frac{200P}{100} \)

\( \text{SI} = 2P \)

Amount \( A = P + \text{SI} = P + 2P = 3P \). This matches the condition that the sum triples.

Conclusion

A sum of money will triple in 20 years on simple interest at a rate of 10% per annum.

Revision Table: Simple Interest Formulas

Additional Information on Simple Interest Calculation

Simple interest is one of the most basic ways to calculate interest on a loan or investment. Unlike compound interest, it does not involve earning interest on previously earned interest. This makes calculations simpler, but usually results in less overall interest earned compared to compound interest over longer periods.

Key points about simple interest:

• The principal amount remains constant for interest calculation.
• Interest earned is directly proportional to the principal, rate, and time.
• It is commonly used for short-term loans or basic calculations.

In this specific problem, understanding that tripling the principal means the interest earned is double the principal is crucial for setting up the equation correctly.