To find the rate of interest for the given problem, we can follow these steps:
1. Identify the given values:
- Initial principal (after 3 years): Rs. 2175
- Final principal (after 5 years): Rs. 2625
- Time period from initial to final amount: 5 years - 3 years = 2 years
2. Calculate the interest accumulated over the 2 years:
- Interest = Final principal - Initial principal
- Interest = Rs. 2625 - Rs. 2175 = Rs. 450
3. Determine the principal amount initially (at the start of the 2-year period):
- Principal_initial = Rs. 2175
4. Calculate the rate of interest per annum:
- We know that the interest accumulated over 2 years is Rs. 450.
- Using the simple interest formula [tex]\( SI = P \times R \times T / 100 \)[/tex], we can find the annual rate of interest [tex]\( R \)[/tex].
- Rearrange the formula to solve for [tex]\( R \)[/tex]: [tex]\( R = (SI \times 100) / (P \times T) \)[/tex]
- Substitute the values into the formula:
[tex]\[
R = \left(\frac{450 \times 100}{2175 \times 2}\right)
\][/tex]
- Simplify:
[tex]\[
R = \left(\frac{45000}{4350}\right) = \left(\frac{100}{9.66666667}\right) \approx 10.344827586206897
\][/tex]
- Therefore, the rate of interest per annum is approximately 10.34%.
In summary, the rate of interest for the given sum of money is approximately 10.34% per annum.
