Question

At a certain rate of interest, the interest after $ 4 $ years on $ 5000 $ rupees principal is $ 1200 $ rupees. What would be the interest of $ 15000 $ rupees at the same rate of interest for the same period? If Pankaj deposits $ 1,50,000 $ rupees in a bank at $ 10 $ p.c.p.a. for two years, what is the total amount he will get from the bank?

Answer 1

Hint: In this question we need to determine the interest of $ 15000 $ rupees at the same rate of interest for the same period i.e., $ 4 $ years and the total amount Pankaj will get from the bank. Here, we will determine the rate of interest by the formula $ I = \dfrac{{P \times T \times R}}{{100}} $ . Then we will determine the interest of $ 15000 $ rupees. Then, we will determine the total amount he gets after $ 2 $ years, by the formula, $ P + \dfrac{{P \times T \times R}}{{100}} $ .

Complete step-by-step answer:
It is given that principal $ \left( P \right) $ is $ 5000 $ rupees.
And, time $ \left( T \right) $ is $ 4 $ years.
Then, total interest $ \left( I \right) $ is $ 1200 $ rupees.
Let $ R $ be the rate of interest.
We know that $ I = \dfrac{{P \times T \times R}}{{100}} $
Therefore, interest on $ 5000 $ rupees after $ 4 $ years $ = \dfrac{{5000 \times 4 \times R}}{{100}} $
 $ I = 200R $
It is given that, total interest $ \left( I \right) $ is $ 1200 $ rupees.
Therefore, $ 1200 = 200R $
 $ R = 6\% $
Therefore, rate of interest = $ 6\% $
Interest on rupees $ 15000 $ rupees is, $ I = \dfrac{{P \times T \times R}}{{100}} $
 $ = \dfrac{{15000 \times 4 \times 6}}{{100}} $
 $ = 600 \times 6 $
 $ = Rs.3600 $
Hence, the interest of $ 15000 $ rupees at the same rate of interest for the same period is $ Rs.3600 $

Now, it also given that Pankaj invested amount $ P = 1,50,000 $
At the rate of interest, $ R $ $ = 10\% $
And, time $ \left( T \right) $ is $ 2 $ years.
Total amount he gets after $ 2 $ years $ = P + \dfrac{{P \times T \times R}}{{100}} $
  $ = P\left( {1 + \dfrac{{2 \times 10}}{{100}}} \right) $
 $ = P\left( {\dfrac{6}{5}} \right) $
 $ = 150000 \times \dfrac{6}{5} $
 $ = 1,80,000 $
Hence, the total amount he will get from the bank is $ Rs.1,80,000 $ .
So, the correct answer is “$ Rs.1,80,000 $”.

Note: In this question it is important to note that when we are facing these kinds of problems, we need to be aware of what is given and what we need to determine. Then we need to be confident about the formula that we use to determine the required.