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SSC GD 2024 PYQ — Question 41

SSC GD Const (English) - 21 Feb 2024 - Shift 2 • Quantitative Aptitude • Q41

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The compound interest (compounding half-yearly) received on Rs. 22000 for 2 years is Rs. 10210.2. What is the interest rate per annum? 

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 20%.

We know that,

A = P(1 + (R/2)/100)2T

here, A = Amount, P = Principal, R = Rate, and T = Time

Amount = Principal + Compound Interest

Amount = 22000 + 10210.2

Amount = Rs.32210.2

Now,

A = P(1 + (R/2)/100)T

⇒ 32210.2 = 22000(1 + (R/2)/100)4

⇒ 32210.2/22000 = (1 + (R/2)/100)4

⇒ 1.4641 = (1 + (R/2)/100)4

⇒ (1 + (R/2)/100) = 41.4641^4\sqrt{1.4641}

⇒ (1 + (R/2)/100) = 1.1

⇒ R/200 = 1.1 - 1

⇒ R/200 = 0.1

⇒ R = 0.1 × 200

⇒ R = 20%

Thus,

The rate of interest per annum is 20%