# In what time will a sum of \[Rs.800\] at $5\% $ p.a. CI amount to $Rs.882$ ?

A.1 year

B.2 year

C.3 year

D.4 year

Answer

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**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.

Additional information:

Difference between compound interest and simple interest:

Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

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