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Joshita has a bank account whose principal is Rs12000 and her bank compounds the interest thrice a year at an interest rate of 15%, how much money did she have in her account at the year's end?
A). 18250.50
B). 28250.50
C). 38250.50
D). 48250.50

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Last updated date: 17th Apr 2024
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Answer
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Hint: Joshita is having a principal amount Rs12000 and her bank compounds the interest thrice a year at an interest rate of 15% and we need to find how much money she will have at the end of the year. To find this amount, we are going to use the formula
\[ \Rightarrow A = P\left[ {{{\left( {1 + \dfrac{r}{{100}}} \right)}^n}} \right]\]

Complete step-by-step solution:
In this question, we are given that Joshita is having a principal amount of Rs12000 and her bank compounds the interest thrice a year at an interest rate of 15% and we need to find how much money she will have at the end of the year.
Now, to find the total amount at the end of the year, we have the formula
\[ \Rightarrow A = P\left[ {{{\left( {1 + \dfrac{r}{{100}}} \right)}^n}} \right]\] - - - - - - - - - - - - - - (1)
Where, $A = $Total Amount, $P = $Principal amount, $r = $ rate of interest and $n = $time period.
Here, we have
$ P = 12000 \\
  r = 15\% \\
  n = 3 \\
  A = ? $
Therefore, substituting these values in equation (1), we get
\[ \Rightarrow A = P\left[ {{{\left( {1 + \dfrac{r}{{100}}} \right)}^n}} \right]\]
\[\Rightarrow A = 12000\left[ {{{\left( {1 + \dfrac{{15}}{{100}}} \right)}^3}} \right] \\
   \Rightarrow A = 12000\left[ {{{\left( {1 + 0.15} \right)}^3}} \right] \\
   \Rightarrow A = 12000\left[ {{{\left( {1.15} \right)}^3}} \right] \\
   \Rightarrow A = 12000\left[ {1.520875} \right] \\
   \Rightarrow A = 18250.50 \]
Hence, Joshita will save Rs18250.50 at the year's end.
Hence, option A is the correct answer.

Note: Here, note that we are taking the value of n=3 because the interest is being compounded thrice a year. If it was given that the interest is being compounded 2 a year, then we had to take the value of n equal to 2.