The difference between the interest earned on the invested amount under compound interest and simple interest at the same rate for 2 years is Rs. 945. If the interest rate is 15% per annum, what is the invested amount?

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Question

This question was previously asked in

UP Police SI (दरोगा) Official PYP (Held On: 21 Nov 2021 Shift 1)

Answer 1

Given:

The difference between the compound interest (CI) and simple interest (SI) for 2 years is ₹945.

Time (t) = 2 years

Compound Interest - Simple Interest = ₹945

Formula used:

Difference between CI and SI for 2 years = \(P \times\left(\frac{R}{100}\right)^2\)

Calculation:

Let the Principal (P) = x

945 = x × \(\left(\frac{R}{100}\right)^2\)

⇒ 945 = x × \(\frac{R^2}{100^2}\)

⇒ 945 = x × \(\frac{15^2}{100^2}\)

⇒ 945 = x × \(\frac{225}{10000}\)

⇒ x = \(\frac{945 × 10000}{225}\)

⇒ x = 42000

∴ The amount invested (Principal) is ₹42,000, and the correct answer is option (2).