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Mathematics

Find the time, in years, in which ₹ 4000 will produce ₹ 630.50 as compound interest at 5 percent p.a. interest being compounded annually.

Compound Interest

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Answer

Given,

P = ₹ 4000

C.I. = ₹ 630.50

r = 5%

A = P + C.I. = ₹ 4000 + ₹ 630.50 = ₹ 4630.50

Let time taken be n years.

By formula,

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

Substituting values we get :

⇒4630.50=4000×(1+5100)n⇒4630.504000=(105100)n⇒9.2618=(2.12)n⇒(2.12)3=(2.12)n⇒n=3.\Rightarrow 4630.50 = 4000 \times \Big(1 + \dfrac{5}{100}\Big)^n \\[1em] \Rightarrow \dfrac{4630.50}{4000} = \Big(\dfrac{105}{100}\Big)^n \\[1em] \Rightarrow \dfrac{9.261}{8} = \Big(\dfrac{2.1}{2}\Big)^n \\[1em] \Rightarrow \Big(\dfrac{2.1}{2}\Big)^3 = \Big(\dfrac{2.1}{2}\Big)^n \\[1em] \Rightarrow n = 3.

Hence, time taken = 3 years.

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