The certain sum amounts to Rs. 9,982.50 in \(2\frac{1}{2}\) years at 12% p.a., interest compounded 10-monthly. The sum (in Rs.) is:

Question

Question

This question was previously asked in

SSC GD 16 Nov 2021 Shift 1 (Official Paper)

Answer 1

Given:

Amount = Rs. 9982.5

Rate = 12%

Time = \(2\frac{1}{2}\) years

Concept used:

A = P(1 + r/100)^t

Here,

A = amount, P = principal or sum, r = rate, t = time

When interest is calculated on a certain monthly

Then,

r = (r/12) × month

t = total month given in the form of year/no. of months

Calculation:

\(2\frac{1}{2}\) years = 30 months [As 1 year = 12 months]

So, t = 30/10 = 3

r = (12/12) × 10 = 10%

Let the sum be Rs. P

Now,

9982.5 = P(1 + 10/100)³

⇒ 9982.5 = P(1 + 1/10)3

⇒ 9982.5 = P(11/10)3

⇒ 9982.5 = 1331P/1000

⇒ P = 9982.5 × (1000/1331)

⇒ P = 7500

So, sum = Rs. 7500

∴ The sum (in Rs.) is Rs 7500.

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