Question

What would be C.I. on Rs. $ 17500 $ at the rate of $ 12 $ p.c.p.a. after $ 2 $ years?
A.Rs. $ 4442 $
B.Rs. $ 4452 $
C.Rs. $ 4462 $
D.Rs. $ 4482 $

Answer 1

Hint: Here, C.I. states for compound interest in which interest on interest which was accumulated last year is also added. Remember Difference between the amount and the principal is the interest. Here we will use the standard formula and by placing the given data find the required term by simplifying the equation.

Complete step-by-step answer:
Given that: Amount, A $ = ? $ Rs.
Principal, $ P = 17500 $ Rs.
Rate of interest, $ r = 12\% $
Term period, $ n = 2 $ years
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 –
 $ A = 17500{\left( {1 + \dfrac{{12}}{{100}}} \right)^2} $
Take LCM (least common multiple) for the above expression –
 $ A = 17500{\left( {\dfrac{{112}}{{100}}} \right)^2} $
Simplify the above expression considering that common factors from the numerator and the denominator cancel each other if possible or then divide the terms in the numerator.
 $ A = 21952{\text{ Rs}}{\text{.}} $
Compound Interest can be given by the difference of the amount and the principal.
 $ I = A - P $
Place the values in the above expression –
 $ I = 21952 - 17500 $
Find the difference of the terms in the above expression –
 $ I = 4452 $ Rs.
From the given multiple choices – the option B is the correct answer.
So, the correct answer is “Option B”.

Note: Always know the difference between the terms simple interest and compound interest and know its standard formula since it is the main and important equation for the correct formula. Be careful during the simplification of the terms, and remove common factors from the numerator and the denominator and be good in multiples till twenty.