A sum of ₹ 3,200 invested at 10 % per cent compounded quarterly amounts to ₹ 3,362. Compute time

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6.Interest

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A sum of ₹ $3,200$ invested at $10 \%$ per cent compounded quarterly amounts to ₹ $3,362.$ Compute the time period (In $years$)

A

$0.5$

B

$1$

C

$2$

D

$0.75$

Solution

(a) $A=P\left(1+\frac{R}{100}\right)^{T} \Rightarrow \frac{3362}{3200}=\left(1+\frac{10}{400}\right)^{4 t}$

$\Rightarrow \frac{1681}{1600}=\left(\frac{41}{40}\right)^{4 t} \Rightarrow\left(\frac{41}{40}\right)^{2}=\left(\frac{41}{40}\right)^{4 t}$

$\Rightarrow \quad 4 t=2 \Rightarrow t=\frac{1}{2}$ year

Standard 13

Quantitative Aptitude

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