A certain amount of money was lent for a period of 1 year 9 months at a rate of 10% per annum compounded annually. If the compound interest is ₹1,460, find the amount of money lent.

Question

Question

This question was previously asked in

SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 02 Aug, 2023 Shift 1)

Answer 1

Given:

Time = 1 year 9 months , rate of interest = 10% , interest amount = ₹1,460,

Concept used:

Compound interest means interest on both principal and interest.

Calculation:

Time = 1 year 9 months = 1\(\frac{3}{4}\) years

= 7/4 years

For the 1st year interest is 10%, and for the next 3/4 years rate of interest should

⇒ 10 × 3/4 = 7.5 %

Let the principal is 100

So interest after 1st year will be,

⇒ 100 × 10/100 = 10

For the next 3/4 year total interest will be ,

⇒ 100 × 7.5 /100 + 10 × 7.5/100

⇒ 7.5 +.75 = 8.25

Total interest after 7/4 years will be ,

⇒ 10 + 8.25 = 18.25

As per the question,

Value of 18.25 = 1460

So the value of 100 units is

⇒ 1460 × 100/18.25

⇒ 80 × 100 = ₹8,000

∴ The correct option is 4

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