Q 2 - At what rate of simple interest a certain aggregate will be multiplied in 15 years?

To determine the rate of simple interest at which a certain principal amount will be multiplied over 15 years, we can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the total amount after time \( t \) years.
- \( P \) is the principal amount (the initial amount).
- \( r \) is the rate of interest per year (as a decimal).
- \( t \) is the time in years.

Let's assume that the amount gets multiplied by \( n \) times, so \( A = nP \).

Substituting this into the formula:

\[
nP = P(1 + rt)
\]

Since \( P \) is common on both sides, it can be canceled out:

\[
n = 1 + rt
\]

Now, solve for \( r \):

\[
r = \frac{n - 1}{t}
\]

Given that the time \( t = 15 \) years:

\[
r = \frac{n - 1}{15}
\]

Thus, the rate of simple interest is \( \frac{n - 1}{15} \times 100 \%\).

If you know the multiplication factor \( n \), you can plug it in to get the specific interest rate.

Would you like to provide the multiplication factor, or do you want further details on this process?

### Relative Questions:
1. What is the multiplication factor \( n \) in this scenario?
2. How does the rate of interest change if the time period is reduced?
3. What happens to the interest rate if the amount is doubled in 10 years?
4. Can this formula be applied to compound interest scenarios?
5. How would the formula change if the interest was compounded annually?

**Tip:** Always ensure that the time period and rate of interest are in the same units (years, months, etc.) when applying formulas.

At what rate of simple interest a certain aggregate will be multiplied in 15 years?

Determine the rate of simple interest needed to multiply a principal amount over 15 years using the simple interest formula. This problem involves key concepts such as multiplication factors and rate calculations. Suitable for students in Grades 9-12.

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