Answer
417.9k+ views
Hint: Here we will use the formula to find the amount A is $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$ where A is the amount, P is principal, R is the rate of interest and n is the time period. Here we will take $n = 1$ for the amount after six months and $n = 2$ for the amount after one year, since the rate of interest is compounded half yearly.
Complete step-by-step answer:
Given that-
Principal, $P = \,{\text{Rs }}60,000$
Rate of interest, $R = 12\% $ per annum
$ \Rightarrow R = 6\% {\text{ }}\;per\,{\text{6 months}}$
(i)After $6$ months
Here, the interest is calculated half-yearly, $\therefore n = 6\;{\text{months = 1}}$
Place values in the formula –
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$
$\therefore A = 60000 \times {\left( {1 + \dfrac{6}{{100}}} \right)^1}$
Take LCM (Least common multiple) and simplify the above equation –
$
\Rightarrow A = 60000 \times {\left( {\dfrac{{100 + 6}}{{100}}} \right)^1} \\
\Rightarrow A = 60000 \times {\left( {\dfrac{{106}}{{100}}} \right)^1} \\
$
Convert the above fraction in the decimal form-
$ \Rightarrow A = 60000 \times (10.6)$
Simplify the above equation-
$ \Rightarrow A = 63600{\text{ Rs}}{\text{.}}$
(ii)After $1$ year
Here, the interest is calculated half-yearly, $\therefore n = 12\;{\text{months = 2}}$
Place values in the formula –
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$
$\therefore A = 60000 \times {\left( {1 + \dfrac{6}{{100}}} \right)^2}$
Take LCM (Least common multiple) and simplify the above equation –
$
\Rightarrow A = 60000 \times {\left( {\dfrac{{100 + 6}}{{100}}} \right)^2} \\
\Rightarrow A = 60000 \times {\left( {\dfrac{{106}}{{100}}} \right)^2} \\
$
Convert the above fraction in the decimal form-
$ \Rightarrow A = 60000 \times {(10.6)^2}$
Simplify the above equation-
$ \Rightarrow A = 67416{\text{ Rs}}{\text{.}}$
Hence, Vasudevan will get Rs. $63600$ and Rs. $67416$ respectively after six months and one year.
Note: Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Remember the difference between simple interest and compound interest and apply its concept wisely. Compound interest is the interest paid for the interest earned in the previous year. Be good in multiples and do simplification carefully. Do not forget to write the unit Rupees after calculation.
Complete step-by-step answer:
Given that-
Principal, $P = \,{\text{Rs }}60,000$
Rate of interest, $R = 12\% $ per annum
$ \Rightarrow R = 6\% {\text{ }}\;per\,{\text{6 months}}$
(i)After $6$ months
Here, the interest is calculated half-yearly, $\therefore n = 6\;{\text{months = 1}}$
Place values in the formula –
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$
$\therefore A = 60000 \times {\left( {1 + \dfrac{6}{{100}}} \right)^1}$
Take LCM (Least common multiple) and simplify the above equation –
$
\Rightarrow A = 60000 \times {\left( {\dfrac{{100 + 6}}{{100}}} \right)^1} \\
\Rightarrow A = 60000 \times {\left( {\dfrac{{106}}{{100}}} \right)^1} \\
$
Convert the above fraction in the decimal form-
$ \Rightarrow A = 60000 \times (10.6)$
Simplify the above equation-
$ \Rightarrow A = 63600{\text{ Rs}}{\text{.}}$
(ii)After $1$ year
Here, the interest is calculated half-yearly, $\therefore n = 12\;{\text{months = 2}}$
Place values in the formula –
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$
$\therefore A = 60000 \times {\left( {1 + \dfrac{6}{{100}}} \right)^2}$
Take LCM (Least common multiple) and simplify the above equation –
$
\Rightarrow A = 60000 \times {\left( {\dfrac{{100 + 6}}{{100}}} \right)^2} \\
\Rightarrow A = 60000 \times {\left( {\dfrac{{106}}{{100}}} \right)^2} \\
$
Convert the above fraction in the decimal form-
$ \Rightarrow A = 60000 \times {(10.6)^2}$
Simplify the above equation-
$ \Rightarrow A = 67416{\text{ Rs}}{\text{.}}$
Hence, Vasudevan will get Rs. $63600$ and Rs. $67416$ respectively after six months and one year.
Note: Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Remember the difference between simple interest and compound interest and apply its concept wisely. Compound interest is the interest paid for the interest earned in the previous year. Be good in multiples and do simplification carefully. Do not forget to write the unit Rupees after calculation.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)