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SSC Selection Post 2022 PYQ — Question 57

SSC Selection Post - Matriculation Level 2022 - 3 Aug 2022 - Shift 1 • Quantitative Aptitude • Q57

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A teacher is giving students the practical experience of compounding. A sum of Rs.1,00,000 is invested at the rate of 10% compound interest by the students for a period of two years. There are two different cases — the given money being compounded annually and being compounded half-yearly. What is the difference between the compound interest earned in the two different cases? (Round off the answer to nearest Rs.)

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Correct answer: B

Explanation

The correct answer is option 2 i.e. Rs.551.

Compounded Annually A =P(1+R100)T P \left(1 + \frac{R}{100} \right)^T 

A=100000(1+10100)2=100000×(1.1)2=100000×1.21=₹1,21,000A = 100000 \left(1 + \frac{10}{100} \right)^2 = 100000 \times (1.1)^2 = 100000 \times 1.21 = ₹1,21,000

CIannual = 121000 - 100000 = ₹21,000

Half-yearly rate = 102=5% \frac{10}{2} = 5\%

Number of periods in 2 years = 2 × 2 = 4

⇒ A=P(1+R2×100)2T=100000(1+5100)4=100000×(1.05)4A = P \left(1 + \frac{R}{2 \times 100} \right)^{2T} = 100000 \left(1 + \frac{5}{100} \right)^4 = 100000 \times (1.05)^4

(1.05)4≈1.21550625(1.05)^4 ≈ 1.21550625

A≈100000×1.21550625=₹1,21,550.63A ≈ 100000 \times 1.21550625 = ₹1,21,550.63

CIhalf yearly = 121550.63 - 100000 = ₹21,550.63

Difference in CI  = 21,550.63 - 21,000 = ₹550.63 ≈\approx ₹551