To determine the principal that will bring an interest of 637 birs at a rate of 9% over 2.5 years, we will follow these steps:
1. Identify the values given:
- Interest ([tex]\(I\)[/tex]): 637 birs
- Annual interest rate ([tex]\(R\)[/tex]): 9%
- Time ([tex]\(T\)[/tex]): [tex]\(2 \frac{1}{2}\)[/tex] years or 2.5 years
2. Convert the interest rate from a percentage to a decimal:
- [tex]\(R = 9\% = \frac{9}{100} = 0.09\)[/tex]
3. Write down the simple interest formula:
- The formula for simple interest is [tex]\(I = P \times R \times T\)[/tex], where [tex]\(I\)[/tex] is the interest, [tex]\(P\)[/tex] is the principal, [tex]\(R\)[/tex] is the rate, and [tex]\(T\)[/tex] is the time.
4. Rearrange the formula to solve for the principal [tex]\(P\)[/tex]:
- Rearranging [tex]\(I = P \times R \times T\)[/tex] to solve for [tex]\(P\)[/tex] gives [tex]\(P = \frac{I}{R \times T}\)[/tex].
5. Substitute the known values into the formula:
- [tex]\(I = 637\)[/tex]
- [tex]\(R = 0.09\)[/tex]
- [tex]\(T = 2.5\)[/tex]
So, [tex]\(P = \frac{637}{0.09 \times 2.5}\)[/tex].
6. Calculate the principal:
- Perform the multiplication in the denominator first:
- [tex]\(0.09 \times 2.5 = 0.225\)[/tex]
- Then divide the interest by this value:
- [tex]\(P = \frac{637}{0.225} \approx 2831.111\)[/tex]
Therefore, the principal that will bring an interest of 637 birs at a rate of 9% in 2.5 years is approximately 2831.11 birs.
