A certain sum is invested at si at 8 percent pa. If this sum triples in 15 yrs find its value

To solve this problem, let's use the formula for simple interest (SI):

\[
A = P(1 + \frac{rt}{100})
\]

Where:
- \( A \) is the final amount after interest,
- \( P \) is the principal amount (initial sum),
- \( r \) is the rate of interest per annum,
- \( t \) is the time in years.

Given:
- The sum triples, so \( A = 3P \).
- The interest rate \( r = 8\% \) per annum.
- The time \( t = 15 \) years.

Substituting the known values into the formula:

\[
3P = P(1 + \frac{8 \times 15}{100})
\]

Simplify the equation:

\[
3P = P(1 + \frac{120}{100})
\]

\[
3P = P(1 + 1.2)
\]

\[
3P = P \times 2.2
\]

Now, divide both sides by \( P \):

\[
3 = 2.2
\]

This equation doesn't hold true, meaning there's an error in interpreting the formula as simple interest. Instead, we need to use the formula correctly.

Let's find the value of the principal, assuming the tripling includes the simple interest itself. The interest earned is \( 2P \) over 15 years. So:

\[
SI = \frac{P \times r \times t}{100}
\]

\[
2P = \frac{P \times 8 \times 15}{100}
\]

Simplifying:

\[
2P = \frac{120P}{100}
\]

\[
2P = 1.2P
\]

This equation again is inconsistent, indicating a possible need for a different approach. 

The consistent way to address this would involve recalculating it using compound interest rather than simple interest, but given the constraints, no sum could possibly triple under simple interest alone. The final principal needs further details to be accurately computed.

Would you like to explore compound interest instead or have further questions on this? Here are related questions:

1. What happens if the interest rate changes during the investment period?
2. How does compound interest compare to simple interest over the same period?
3. What if the sum doubles instead of triples?
4. How do inflation and other economic factors affect simple interest investments?
5. What would be the principal sum if the time period was halved?

**Tip:** Double-check the interest type (simple vs. compound) when dealing with significant growth (like doubling or tripling) over long periods.

Explore how investments grow differently with simple and compound interest. Solve the problem where a sum triples in 15 years with an 8% annual interest rate using detailed mathematical formulas and explanations.

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