To find the principal amount that amounts to Rs. 530 in 2 years at an interest rate of 3% per annum, we can use the simple interest formula. The formula for the amount [tex]\( A \)[/tex] is:
[tex]\[ A = P + \left( \frac{P \times R \times T}{100} \right) \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount (Rs. 530)
- [tex]\( P \)[/tex] is the principal amount (the value we need to find)
- [tex]\( R \)[/tex] is the rate of interest per annum (3%)
- [tex]\( T \)[/tex] is the time period in years (2 years)
We need to rearrange this formula to solve for [tex]\( P \)[/tex].
Starting with the given formula:
[tex]\[ A = P + \left( \frac{P \times R \times T}{100} \right) \][/tex]
We can factor out [tex]\( P \)[/tex] from the terms on the right-hand side:
[tex]\[ A = P \left( 1 + \frac{R \times T}{100} \right) \][/tex]
Now, solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{A}{\left( 1 + \frac{R \times T}{100} \right)} \][/tex]
Substitute the given values into the formula:
- [tex]\( A = 530 \)[/tex]
- [tex]\( R = 3 \)[/tex]
- [tex]\( T = 2 \)[/tex]
[tex]\[ P = \frac{530}{\left( 1 + \frac{3 \times 2}{100} \right)} \][/tex]
[tex]\[ P = \frac{530}{\left( 1 + \frac{6}{100} \right)} \][/tex]
[tex]\[ P = \frac{530}{1 + 0.06} \][/tex]
[tex]\[ P = \frac{530}{1.06} \][/tex]
[tex]\[ P \approx 500.0 \][/tex]
Therefore, the principal amount that amounts to Rs. 530 in 2 years at a 3% interest rate per annum is Rs. 500.0.
