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(a) Rs. 120

(b) Rs. 121

(c) Rs. 122

(d) Rs. 123

Answer
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Before starting with the question, let us know about interest.

Interest in the financial term is the amount that a borrower pays to the lender along with the repayment of the actual principal amount.

Broadly, there are two kinds of interest, first is the simple interest, and the other is the compound interest.

Now let us move to the case in which the interest is compounded half-yearly. The rate of interest is 5% per annum, and the formula that is to be used is $ I=P{{\left( 1+\dfrac{r}{100n} \right)}^{nt}}-P $ , where n is number of times the interest is compounded yearly, which is 2 in our case.

First, let us find the interest on the principal deposited on January 1, which is deposited for 1 year.

$ I=1600{{\left( 1+\dfrac{5}{100\times 2} \right)}^{2\times 1}}-1600 $

$ I=1600\left( {{\left( \dfrac{41}{40} \right)}^{2}}-1 \right)=1600\left( \dfrac{81}{1600} \right)=\text{Rs}\text{. }81 $

Now, let us calculate the interest for the principal deposited on July 1, for which $ t=\dfrac{1}{2} $ .

$ I=1600{{\left( 1+\dfrac{5}{100\times 2} \right)}^{2\times \dfrac{1}{2}}}-1600 $

\[\Rightarrow I=1600\left( \dfrac{41}{40}-1 \right)=1600\times \dfrac{1}{40}=\text{Rs}\text{. }40\]

Now, to get the total interest, we will add the two results.

$ \text{Total interest}=81+40=\text{Rs}\text{. 121} $

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