Answer

Verified

413.4k+ views

**Hint**: Start by using the formula that $ I=P{{\left( 1+\dfrac{r}{100n} \right)}^{nt}}-P $ for the finding the amount when the interest is compounded half yearly. First, find the interest on the principal deposited on January 1, which is deposited for 1 year and then for the principal deposited on July 1, for which $ t=\dfrac{1}{2} $ . Add the two interests to get the answer.

**:**

__Complete step-by-step answer__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} $

**So, the correct answer is “Option B”.**

**Note**: Be careful with the calculations and solving part as there is a possibility of making a mistake in the calculations. It is recommended to learn all the basic formulas related to simple as well as compound interests as they are very much useful in the problems related to money exchange. Also, don’t get confused and take the time period t for both the cases to be 1 years, make sure that you take $ t=\dfrac{1}{2} $ for the second case.

Recently Updated Pages

How do you evaluate cos left dfrac13pi 12 right class 10 maths CBSE

How do you rewrite the inequality left 11 2x right class 10 maths CBSE

How do you solve 4 3x 025 class 10 maths CBSE

How do you find the zeros of x3 3x2 + 6x 18 class 10 maths CBSE

Consider the following statements in respect of the class 10 maths CBSE

How do you factor 2x3 + 3x2 8x 12 class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail