Question

30,000 is invested for some period at 8% per annum to earn 2400 as the simple interest. if the same sum is invested for the same period at the same rate of interest compounded half yearly find the compound interest​

Answer 1

Step-by-step explanation:

Principal ( P )=₹ 30000

Rate (R)=8 % p.a.

Simple interest =₹ 2400

$\color{red} \text{ ∴ \: Period \( \tt (n)=\dfrac{\text { S.I. } \times 100}{\text { P } \times \text { R }}=\dfrac{2400 \times 100}{30000 \times 8}=1 \: \: \: \: year \)}$

Now, when interest is compounded,

the principal (P)=₹ 30000

Rate (R)=8 % p.a. =4 % half yearly

Period (n)=1 year =2 half years

$\color{darkviolet}\[ \begin{array}{l} \tt \therefore \text { Amount }(A)=P\left(1+\dfrac{R}{100}\right)^{n}=₹ 30000\left(1+\dfrac{4}{100}\right)^{2}=₹ 30000 \times\left(\dfrac{26}{25}\right)^{2} \\ \\ \tt=₹ 30000 \times \dfrac{26}{25} \times \dfrac{26}{25}=₹ 32448 \\ \\ \tt \therefore \text { Compound interest }=A-P \\ \\ \tt =₹ 32448-30000=₹ 2448 \end{array} \]$