Courses
Courses for Kids
Free study material
Offline Centres
More
Last updated date: 06th Dec 2023
Total views: 279.9k
Views today: 2.79k

# In what time will a sum of $Rs.800$ at $5\%$ p.a. CI amount to $Rs.882$ ?A.1 yearB.2 year C.3 yearD.4 year

Verified
279.9k+ views
Hint: Compound Interest: Compound interest is interest on interest. Addition of the interest in the principal amount. Or reinvesting the interest.
As we know that
$\Rightarrow C.I. = P{\left( {1 + \dfrac{r}{{100}}} \right)^T} - P$
Here
CI=compound interest
P=principal
r=rate of interest
T=time
As we have found time for a given question. so , I will keep the value in the given equation and try to solve step by step as maintained below.

Complete step by step solution:
Given,
Principal, $P = Rs.800$
Amount, $A = Rs.882$
Rate, $R = 5\%$
Time, $T = ?$
Rate, R=?
Formula of compound interest,
$\Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^T}$
Put the values in the formula,
$\Rightarrow 882 = 800{\left( {1 + \dfrac{5}{{100}}} \right)^T}$
Simplify
$\Rightarrow \dfrac{{882}}{{800}} = {\left( {1 + \dfrac{1}{{20}}} \right)^T}$
$\Rightarrow \dfrac{{441}}{{400}} = {\left( {\dfrac{{20 + 1}}{{100}}} \right)^T}$
$\Rightarrow \dfrac{{441}}{{400}} = {\left( {\dfrac{{21}}{{100}}} \right)^T}$
$\Rightarrow {\left( {\dfrac{{21}}{{20}}} \right)^2} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
The Bases of both sides are the same so bases are cancelled out.
$\Rightarrow T = 2years$
So the answer is (B) $2year$ .
So, the correct answer is “Option B”.

Note: Compound interest earned or paid on both the principal and previously earned interest. For annually compound interest means “once in a year”, half yearly means “twice in the year”, quarterly means “four times in the year”. Compound interest is always more than simple interest for a given period of time.