Maths / Comparing Quantities / Compound Interest Half Yearly

QUESTION

A sum of Rs. 3,200 invested at 10% per annum compounded quarterly amounts tc Rs. 3,362. Compute the time period.

EXPLANATION
Explain TypeExplanation Content
Text

Here P = Rs. 3,200

R = 10% per annum  $\dpi{100} =\frac {10}{4}$ % quarterly

T = ?

A = Rs. 3,362

$\dpi{100} \Rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3,362=3,200 \left ( 1+\frac {10}{400} \right )^n \\\\\ \Rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac {3,362}{3,200}=\left ( \frac {410}{400} \right )^n \: \: \: \: \: \: \: \: \: \Rightarrow \: \: \: \: \: \: \: \frac {1,681}{1,600}=\left ( \frac {41}{40} \right )^n \: \: \: \: \: \: \: \Rightarrow \: \: \: \: \: \: \: \: \: \: \left ( \frac {41}{40} \right )^2=\left ( \frac {41}{40} \right )^n \\\\\ \Rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n=2 \\\\ \Rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: T=2\: \: quarter \: years \\\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: T=2 \times 3 = 6 \: \: months$

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