A sum of ₹ 3,200 invested at 10 % per annum c | vedclass

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(A) The formula for compound interest is $A = P(1 + \frac{R}{n 	imes 100})^{nt}$,where $A$ is the amount,$P$ is the principal,$R$ is the annual inter

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$0.5$

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(A) The formula for compound interest is $A = P(1 + \frac{R}{n 	imes 100})^{nt}$,where $A$ is the amount,$P$ is the principal,$R$ is the annual interest rate,$n$ is the number of times interest is compounded per year,and $t$ is the time in years.Given: $P = 3200$,$A = 3362$,$R = 10$,and $n = 4$ (quarterly).Substituting the values: $3362 = 3200(1 + \frac{10}{400})^{4t}$.$\frac{3362}{3200} = (1 + \frac{1}{40})^{4t}$.$\frac{1681}{1600} = (\frac{41}{40})^{4t}$.Since $41^2 = 1681$ and $40^2 = 1600$,we have $(\frac{41}{40})^2 = (\frac{41}{40})^{4t}$.Equating the exponents: $4t = 2$.Therefore,$t = \frac{2}{4} = 0.5$ years.

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

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