To find the sum of money (principal) that would produce Rs 5000 as interest in 2 years at an interest rate of [tex]\( 10\% \)[/tex] per annum using simple interest, follow these steps:
1. Identify the given values:
- Interest earned, [tex]\( I = Rs 5000 \)[/tex]
- Annual interest rate, [tex]\( r = 10\% \)[/tex] or 0.1 in decimal form
- Time period, [tex]\( t = 2 \)[/tex] years
2. Use the simple interest formula:
[tex]\[
I = P \times r \times t
\][/tex]
Here, [tex]\( I \)[/tex] is the interest, [tex]\( P \)[/tex] is the principal (the amount of money lent), [tex]\( r \)[/tex] is the annual interest rate, and [tex]\( t \)[/tex] is the time period in years.
3. Rearrange the formula to solve for the principal [tex]\( P \)[/tex]:
[tex]\[
P = \frac{I}{r \times t}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
P = \frac{5000}{0.1 \times 2}
\][/tex]
5. Calculate the denominator first:
[tex]\( 0.1 \times 2 = 0.2 \)[/tex]
6. Now, divide the interest by the calculated denominator:
[tex]\[
P = \frac{5000}{0.2} = 25000
\][/tex]
Therefore, the sum of money (principal) that would produce Rs 5000 as interest in 2 years at an interest rate of [tex]\( 10\% \)[/tex] per annum is Rs 25000.
