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A man deposited Rs.10000 in a bank with an interest rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the amount after 20 years.

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Hint: Initially find the interest of the first year by using the given data. And by using the interest we can also find the amount that has been deposited in the 15th year and this helps to calculate the amount after 20 years.

Here from the data it is given that a man deposited Rs.10000 in a bank with an interest rate of 5% simple interest annually.
So, it is known that in simple interest, the interest remains the same in all years.
This means if we find interest in the first year then the interest will be the same for all years.
Now let us find interest for first year
$I = PTR$
Here I is the interest, P= Rs.10000, R=5% and t=1(for one year)
$\begin{gathered}
   \Rightarrow I = 10000 \times 5\% \times 1 \\
   \Rightarrow I = 10000 \times \dfrac{5}{{100}} \\
   \Rightarrow I = 500 \\
\end{gathered} $
So interest of first year =Rs.500
Therefore interest for all years is also Rs.500 as it is simple interest used by the person.
Hence,
Amount in 1st year=Rs.10000
Amount in 2nd year = Amount in 1st year +Interest = Rs.10000 + Rs.500 =Rs.10500
Amount in 3rd year = Amount in 2nd year + Interest = Rs10500 + Rs.500 =Rs.11000
Hence our series is
          Rs.10000, Rs.10500, Rs.11000 …
If we observe the series it is of AP
Where a=10000 and d=500 (interest is 500 which is common for all years)
Or else d=a2-a1 which implies d=10500-10000=500
There d=500
Now here we need to find amount in 15th year, as the series are in AP let us use nth term of AP where n=15
So, nth term of AP
$ \Rightarrow {a_n} = a + (n - 1)d$
Amount in 15th year = $a + (n - 1)d$
                                   =10000 + (15-1)500
                                  =10000+14(500)
                                =17000
Therefore amount in 15th year is Rs.17000
And also here we need to find amount after 20 year
 i.e. we need to calculate ${a_n}$ value where n=21
Amount after 20 year = ${a_n}$
                                      = $a + (n - 1)d$
                                      =10000 + (20-1)500
                                       =10000+19(500)
                                      =20,000
Therefore amount after 20 years is Rs. 20,000

Note: As the person has taken simple interest, so for every year the interest will be the same .So find interest for 1st year which will be the same for all other years. Later adding interest to the previous year amount we get the present year amount. As interest is common the amount will be in AP series. Make a note that the series is of AP so we have used the nth term of AP formula to find amount for 15th year and amount after 20 years.
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