To find the principal that will amount 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 accumulated amount (A) in terms of the principal (P), rate of interest per annum (r), and time (t) in years is:
[tex]\[ A = P(1 + rt) \][/tex]
Where:
- [tex]\( A \)[/tex] is the final amount after interest,
- [tex]\( P \)[/tex] is the principal amount (initial amount),
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the time the money is invested for (in years).
Given:
- [tex]\( A = 530 \)[/tex] (the amount after 2 years),
- [tex]\( t = 2 \)[/tex] years,
- [tex]\( r = \frac{3}{100} = 0.03 \)[/tex] (converting percentage to a decimal).
We need to find the principal [tex]\( P \)[/tex]. Rearrange the formula to solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{A}{1 + rt} \][/tex]
Substitute the given values into the equation:
[tex]\[ P = \frac{530}{1 + 0.03 \cdot 2} \][/tex]
Calculate the denominator:
[tex]\[ 1 + 0.03 \cdot 2 = 1 + 0.06 = 1.06 \][/tex]
Now, divide 530 by 1.06 to find the principal:
[tex]\[ P = \frac{530}{1.06} = 500.0 \][/tex]
So, the principal that amounts to Rs. 530 in 2 years at an interest rate of 3% per annum is Rs. 500.
