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Mathematics

A sum of money, lent out at 10% C.I. compounded yearly becomes ₹ 6050 in 2 years. The sum lent is :

  1. ₹ 7260

  2. ₹ 4000

  3. ₹ 5000

  4. ₹ 7320.50

Compound Interest

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Answer

Given,

r = 10%

n = 2 years

Let sum of money lent be ₹ x.

P = ₹ x

A = ₹ 6050

By formula,

A=P(1+r100)nA = P\Big(1 + \dfrac{r}{100}\Big)^n

Substituting values we get :

⇒6050=x(1+10100)2⇒6050=x×(110100)2⇒6050=x×(1110)2⇒6050=121x100⇒x=6050×100121⇒x=₹5000.\Rightarrow 6050 = x\Big(1 + \dfrac{10}{100}\Big)^2 \\[1em] \Rightarrow 6050 = x \times \Big(\dfrac{110}{100}\Big)^2 \\[1em] \Rightarrow 6050 = x \times \Big(\dfrac{11}{10}\Big)^2 \\[1em] \Rightarrow 6050 = \dfrac{121x}{100} \\[1em] \Rightarrow x = \dfrac{6050 \times 100}{121} \\[1em] \Rightarrow x = ₹ 5000.

Hence, Option 3 is the correct option.

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