A man deposited \[{\text{Rs 10000}}\] in a bank at the rate of \[{5\% }\] simple interest annually. Find the amount in $ 15th $ year since he deposited the amount and also calculate the total amount after $ 20 $ years.

Hint: Here we use the concept of Simple Interest.
 $ {\text{Simple Interest}}\left( {{\text{SI}}} \right){\text{ = }}\dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{{\text{100}}}} $
Where P is the Principal amount
T is the time period
R is rate of interest per annum
 $
  {\text{Amount = Principal amount + Simple Interest}} \\
  {\text{A = P + SI}} \;
  $

Complete step-by-step answer:
Given: Principal amount is \[{\text{Rs 10000}}\]
Rate of interest per annum is \[{5\% }\]
We need to find the amount in $ 15th $ year and total amount after $ 20 $ years.
Simple interest for $ 15 $ years is ,
 $
  {\text{Simple Interest}}{\left( {{\text{SI}}} \right)_{{\text{15 years}}}}{\text{ = }}\dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{{\text{100}}}} \\
   \Rightarrow {\text{Simple Interest}}{\left( {{\text{SI}}} \right)_{{\text{15 years}}}}{\text{ = }}\dfrac{{{\text{10000}} \times {\text{15}} \times {\text{5}}}}{{{\text{100}}}} \\
   \Rightarrow {\text{Simple Interest}}{\left( {{\text{SI}}} \right)_{{\text{15 years}}}}{\text{ = 7500}} \;
  $
Amount $ 15 $ years since is,
 $
  {\text{Principal + S}}{{\text{I}}_{{\text{15 years}}}} \\
   \Rightarrow {\text{10000 + 7500}} \\
   \Rightarrow {\text{17500}} \;
  $
Therefore amount in $ 15th $ year since deposited is $ {\text{Rs 17500}} $
So, the correct answer is “ $ {\text{Rs 17500}} $ ”.

Simple interest for $ 20 $ years is ,
 $
  {\text{Simple Interest}}{\left( {{\text{SI}}} \right)_{{\text{20 years}}}}{\text{ = }}\dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{{\text{100}}}} \\
   \Rightarrow {\text{Simple Interest}}{\left( {{\text{SI}}} \right)_{{\text{20 years}}}}{\text{ = }}\dfrac{{{\text{10000}} \times {\text{20}} \times {\text{5}}}}{{{\text{100}}}} \\
   \Rightarrow {\text{Simple Interest}}{\left( {{\text{SI}}} \right)_{{\text{20 years}}}}{\text{ = 10000}} \;
  $
Amount after $ 20 $ years is,
 $
  {\text{Principal + S}}{{\text{I}}_{{\text{20 years}}}} \\
   \Rightarrow {\text{10000 + 10000}} \\
   \Rightarrow 200{\text{00}} \;
  $
Therefore amount after $ 20 $ years is $ {\text{Rs 20000}} $
So, the correct answer is “ $ {\text{Rs 20000}} $ ”.

Note: In the questions involving the concept of Simple Interest we need to have knowledge about the formula and the terms involved in it. Applying the given information and solving accordingly by applying the appropriate formulae will help us to find the required value.