To determine the time in which Rs 300 will amount to Rs 405 at an interest rate of 4%, we can use the simple interest formula. This formula is:
[tex]\[ A = P(1 + rt) \][/tex]
where:
- [tex]\( A \)[/tex] is the final amount (Rs 405)
- [tex]\( P \)[/tex] is the principal amount (Rs 300)
- [tex]\( r \)[/tex] is the annual interest rate (4% per year or 0.04 in decimal form)
- [tex]\( t \)[/tex] is the time in years
We need to rearrange this formula to solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{A}{P \cdot (1 + rt)} - 1 \][/tex]/ r
Given the values:
- [tex]\( A = 405 \)[/tex]
- [tex]\( P = 300 \)[/tex]
- [tex]\( r = 0.04 \)[/tex]
Substitute these values into the rearranged formula:
[tex]\[ t = \frac{405}{300 \cdot (1 + 0.04t)} - 1 \][/tex]/ 0.04
From this relationship, we can solve for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{405}{300} - 1 ] / 0.04 \][/tex]
[tex]\[ t = \frac{405}{300} ] - 1 / 0.04 \][/tex]
[tex]\[ t = 35/3 years ]
After performing the calculations, we find that:
\[ t = 8.75 \][/tex]
Thus, the time required for Rs 300 to amount to Rs 405 at a rate of 4% per annum is [tex]\( 8.75 \)[/tex] years, which corresponds to
Answer: [tex]\( d \)[/tex] [tex]\(\ = \frac{35}{4}\)[/tex] years
