Question

What amount will sum up to Rs. $6,655$ at $10\% $ p.a. in C.I. in $3$ years?
A. $4000$
B. $6000$
C. $5000$
D. $7000$

Answer 1

Hint: Here, C.I. stands for the compound interest. Compound interest is the interest occurred on the earned interest in the previous year. Here we will use the standard formula for the compound interest and simplify the expression placing the given data and simplifying for the required resultant value.

Complete step by step answer:
Given that: Amount, A $ = 6655$Rs, Term period, $n = 3$ years and 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 –
$6655 = P{\left( {1 + \dfrac{{10}}{{100}}} \right)^3}$
Remove common factors from the numerator and the denominator and simplify the fraction first in the above expression –
$6655 = P{\left( {1 + \dfrac{1}{{10}}} \right)^3}$

Take LCM (least common multiple) for the above expression –
$6655 = P{\left( {\dfrac{{11}}{{10}}} \right)^3}$
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.
$P = \left( {\dfrac{{10 \times 10 \times 10}}{{11 \times 11 \times 11}}} \right) \times 6655$
Simplify the above expression considering that common factors from the numerator and the denominator cancel each other.
$ \therefore P = 5000$ Rs.

Hence, option C is the correct answer.

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