Question

In what time will Rs. $ 4000 $ amount to Rs. $ 5,324 $ at $ 10\% $ p.a. in CI?
A. $ 1 $ years
B. $ 2 $ years
C. $ 3 $ years
D. $ 4 $ years

Answer 1

Hint: Here, C.I. stands for compound interest in which interest on interest which was accumulated last year is also considered. Interest can be defined as the monetary charge for the privilege for borrowing someone else’s money. Here we will use the standard formula and place the given data and find the required term simplifying the equation.

Complete step-by-step answer:
Given that: Amount, A $ = 5324 $ Rs.
Principal, $ P = 4000 $ Rs.
Rate of interest, $ r = 10\% $
Here we will use the formula for the compound interest which is given by –
 $ A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} $
Place the given values in the above equation –
 $ 5324 = 4000{\left( {1 + \dfrac{{10}}{{100}}} \right)^n} $
Remove common factors from the numerator and the denominator and simplify the fraction first in the above expression –
 $ 5324 = 4000{\left( {1 + \dfrac{1}{{10}}} \right)^n} $
Take LCM (least common multiple) for the above expression –
 $ 5324 = 4000{\left( {\dfrac{{11}}{{10}}} \right)^n} $
The above expression can be re-written as –
 $ 5324 = 4000{\left( {1.1} \right)^n} $
Make the required term the subject and move other terms on the opposite side. Term multiplicative on one side is moved to the opposite side then it goes to the denominator and vice-versa.
 $ {\left( {1.1} \right)^n} = \dfrac{{5324}}{{4000}} $
Simplify the above expression considering that common factors from the numerator and the denominator cancel each other if possible or divide it.
 $ {\left( {1.1} \right)^n} = 1.331 $
We know that the $ {11^3} = 1331 $ and so above expression can be re-written as –
 $ {\left( {1.1} \right)^n} = {\left( {1.1} \right)^3} $
When bases are the same, powers are equal.
 $ \Rightarrow n = 3 $ years
From the given multiple choices – the option C is the correct answer.
So, the correct answer is “Option C”.

Note: Always know the difference between the simple and compound interest and know its standard formula as it is the main and important equation for the correct formula. Amount can be defined as the value which is the sum of the principal value and the interest occurred during the term period.