Question

In what time will $Rs.1,60,000$ become $Rs1,94,481$ if interest is $10\%$ p.a. compounded semi-annually?

• A. 2 years
• B. 2 half years
• C. 4 years
• D. 3 years

Answer 1

Answer: (A)

According to question,

Principal $\left(P\right)=Rs.1,60,000$

Total amount $\left(A\right)=Rs1,94,481$

Rate of interest $\left(R\right)=10\%$ per annum.

$\Rightarrow$ Rate of interest $\left(R\right)=5\%$, compounded half yearly.

Since, the Total amount on compound interest is,

$A=P(1+\frac{R}{100}{)}^n$

$\Rightarrow Rs1,94,481=Rs.1,60,000(1+\frac{5}{100}{)}^n$

$\Rightarrow \frac{1,94,481}{1,60,000}=(1+\frac{1}{20}{)}^n$

$\Rightarrow \frac{{21}^4}{{20}^4}=(\frac{21}{20}{)}^n$

$\Rightarrow (\frac{21}{20}{)}^4=(\frac{21}{20}{)}^n$

Since, bases are equal then the powers also be equal.

$\Rightarrow n=4$

i.e., $4$ half years. [Since, amount was calculate on compounded half-yearly].

$=2$ years.

Therefore, the time $\left(T\right)=2$ years.

Hence, Option A is correct.