$\begin{array}{1 1}Rs. 16,000 \:and\:Rs. 2,94000 \\ Rs. 17,000 \:and\:Rs. 29000 \\Rs. 16,500 \:and\:Rs. 2,95000 \\ Rs. 17,000 \:and\:Rs. 2,95000 \end{array} $

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- $n^{th}$ term of an A.P., $t_n=a+(n-1)d$
- Sum of $n$ terms of an A.P., $S_n=\large\frac{n}{2}$$\big[2a+(n-1)d\big]$

Given that the initial deposit $=Rs.10,000$

Interest= 5% (simple interest).

Interest after one year $=\large\frac{5}{100}$$\times 10000$

$\qquad\qquad\:=500$

$\therefore$ After one year the ampount $=10,000+500=10500$

Similarly after two years the amount $=10,000+2\times 500=11,000$

and so on.

This amount increases in A.P.

$\therefore$ The amount in 15$^{th}$ years is $15^{th}$ term of the series

$10,000+10,500+11,000+.......$ which is A.P. with

first term $=a=10,000$ and common difference $=500$

We know that $n^{th}$ term of an A.P., $t_n=a+(n-1)d$

$\therefore$ The amount in $15^{th}$ year $=t_{15}= 10,000+(15-1)500\big]$

$=10,000+7000=Rs.17,000$

Step 2

The total amount after $20$ years is the sum of $20$ terms of the above series.

We know that the sum of $n$ terms of an A.P., $S_n=\large\frac{n}{2}$$\big[2a+(n-1)d\big]$

$\therefore$ $S_{20}=\large\frac{20}{2}$$\big[2\times 10000+(20-1)500\big]$$=295000.$

$i.e.,$ Total amount after 20 years $=Rs. 2,95,000$

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