Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

18. If a sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years, find the rate of interest.

a. [tex]$15 \%$[/tex]
b. [tex]$12 \%$[/tex]

Sagot :

GinnyAnswer
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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.