Answered

IDNLearn.com provides a seamless experience for finding the answers you need. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

(i) [tex]$C_l = P(1 + \frac{R}{100})$[/tex]
(ii) [tex]$C_i = P\left[\left(1 + \frac{R}{200}\right)^T - 1\right]$[/tex]
(iii) [tex]$C_i = P\left[\left(1 + \frac{R}{100}\right)^T - 1\right]$[/tex]
(iv) [tex]$C_l = P\left(1 + \frac{R}{100}\right)^T - 1$[/tex]

(a) साधारण व्याज र चक्रीय व्याज पत्ता लगाउनुहोस्। वार्षिक [tex]$20\%$[/tex] ब्याजदरले 2 वर्षमा हुने वार्षिक मिश्रित ब्याज र अर्धवार्षिक मिश्रित ब्याज पत्ता लगाउनुहोस्।

Find the simple interest and compound interest on a sum of money at an annual interest rate of [tex]$20\%$[/tex] over 2 years, compounded annually and semi-annually.

(i) Write down the formula for calculating the yearly compound interest.
(ii) उक्त धनराशि पत्ता लगाउनुहोस्। Find the sum of money.
(iii) अर्धवार्षिक र वार्षिक मिश्रित ब्याजको अन्तर पत्ता लगाउनुहोस्। Find the difference between half-yearly and yearly compound interest.

Note: वार्षिक चक्रीय व्याजदरमा कुनै रकमको मिश्रधन 2 वर्ष र 3 वर्षमा क्रमशः र. 23,328 र र. [tex]$25,194.24$[/tex] हुन्छ। The compound interest on a sum of money over 2 years and 3 years is Rs. 23,328 and Rs. [tex]$25,194.24$[/tex] respectively.

(a) वार्षिक चक्रीय मिश्रधन पत्ता लगाउने सूत्र लेख्नुहोस्। Write down the formula to find the annual compound interest.

Sagot :

GinnyAnsweridn
Sure, let's go through each part of the question step-by-step.

### Given Data:
- Principal amount, [tex]\(P = \text{Rs. }18,082\)[/tex]
- Annual rate of interest, [tex]\(R = 20\%\)[/tex]
- Time, [tex]\(T = 2\)[/tex] years

### Formulas Involved:
1. Yearly Compound Interest:
[tex]\[ CI_{\text{yearly}} = P \left( \left(1 + \frac{R}{100}\right)^T - 1 \right) \][/tex]

2. Half-Yearly Compound Interest:
[tex]\[ CI_{\text{half-yearly}} = P \left( \left(1 + \frac{R}{200}\right)^{2T} - 1 \right) \][/tex]

### Step-by-Step Solution:

#### (a) Calculation of Yearly Compound Interest:
Using the formula for yearly compound interest:
[tex]\[ CI_{\text{yearly}} = P \left( \left(1 + \frac{R}{100}\right)^T - 1 \right) \][/tex]

Substitute the given values into the formula:
[tex]\[ CI_{\text{yearly}} = 18082 \left( \left(1 + \frac{20}{100}\right)^2 - 1 \right) \][/tex]

After performing the calculation, we find that the yearly compound interest is:
[tex]\[ CI_{\text{yearly}} \approx \text{Rs. } 7956.08 \][/tex]

#### (b) Calculation of Half-Yearly Compound Interest:
Using the formula for half-yearly compound interest:
[tex]\[ CI_{\text{half-yearly}} = P \left( \left(1 + \frac{R}{200}\right)^{2T} - 1 \right) \][/tex]

Substitute the given values into the formula:
[tex]\[ CI_{\text{half-yearly}} = 18082 \left( \left(1 + \frac{20}{200}\right)^{4} - 1 \right) \][/tex]

After performing the calculation, we find that the half-yearly compound interest is:
[tex]\[ CI_{\text{half-yearly}} \approx \text{Rs. } 8391.86 \][/tex]

#### (c) Difference Between Half-Yearly and Yearly Compound Interest:
To find the difference between the half-yearly and yearly compound interest:
[tex]\[ \text{Difference} = CI_{\text{half-yearly}} - CI_{\text{yearly}} \][/tex]

Using the values obtained:
[tex]\[ \text{Difference} \approx 8391.86 - 7956.08 = \text{Rs. } 435.78 \][/tex]

### Conclusion:
1. Yearly Compound Interest after 2 years: Rs. 7956.08
2. Half-Yearly Compound Interest after 2 years: Rs. 8391.86
3. Difference between Half-Yearly and Yearly Compound Interest: Rs. 435.78
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.