Question

Shanta borrowed Rs.6000 from the state Bank of India for 3 years 8 months at 12% per annum. What amount will clear off her debt?

Answer 1

Hint- In order to find the debit amount, first we will calculate the simple interest and simple interest can be given as $\dfrac{{P \times R \times T}}{{100}}$ , So by adding the simple interest and principal amount we will get the debt amount.

Complete step-by-step answer:

Given that principle amount is Rs. 6000
 Rate is 12%
 And the time is 3 years 8 months.
Let us convert the months in years.
$
  \because 12{\text{months}} = 1{\text{year}} \\
   \Rightarrow 1{\text{month}} = \dfrac{1}{{12}}{\text{year}} \\
   \Rightarrow 8{\text{month}} = 8 \times \dfrac{1}{{12}}{\text{year}} \\
   \Rightarrow 8{\text{month}} = \dfrac{2}{3}{\text{year}} \\
 $
So the total time is 3 years + $\dfrac{2}{3}$ year = $\left( {3 + \dfrac{2}{3}} \right){\text{year = }}\left( {\dfrac{{11}}{3}} \right){\text{year}}$
 As we know that
 Simple interest = $\dfrac{{P \times R \times T}}{{100}}$
Substitute the value of principal amount, rate and time, so we obtain
Simple interest:
$
   = \dfrac{{P \times R \times T}}{{100}} \\
   = \dfrac{{6000 \times 12 \times \dfrac{{11}}{3}}}{{100}} \\
   = \dfrac{{6000 \times 12 \times 11}}{{300}} \\
   = 240 \times 11 \\
   = Rs.2640 \\
 $
Therefore the interest will be Rs. 2640
And the debt amount = principal amount + simple interest
Debt amount \[ = Rs.6000 + Rs.2640 = Rs.8640\]
Hence, the debt amount = Rs.8640

Note- In order to solve such a question always the time to be substituted in the formula of simple interest must be in years. So if the time is given in months or days first convert it into years before finding simple interest. Also students must remember the formula for simple interest.