Question

A certain sum amounts to ₹1331 in 3\2 years at 20% p.a. compound interest compounded half yearly. Determine the sum.​

Answer 1

Answer:

To calculate compound interest for half yearly, the rate percent = 20 % it become half and time become double that is 1.5 to 3. = Rs 1000. Hence the Sum is Rs 1000.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\color{red} \pmb{\[ \begin{array}{l} \tt A=₹ 1331 \\ \\ \tt T=1 \frac{1}{2} \text { year or } \frac{3}{2} \text { year } \\ \\ \tt R=20 \% \end{array} \]}$

But for half yearly,

$\color{olive} \pmb{\[ \begin{array}{l} \tt T=\frac{3}{2} \times 2 \\ \\ \tt =3 \\ \text{And \( \tt R=\dfrac{20}{2} \) \[ =10 \% \]} \end{array} \] }$

We know that,

$\color{darkcyan} \pmb{\[ \begin{array}{l} \tt A=P\left(1+\dfrac{R}{100}\right)^{T} \\ \\ \tt 1331=P\left(1+\dfrac{10}{100}\right)^{3} \\ \\ \tt 1331=P\left(\dfrac{11}{10}\right)^{3} \\ \\ \tt 1331=P \times \dfrac{1331}{1000} \\ \\ \tt P=₹ 1000 \end{array} \]}$

Hence the sum =₹ 1000.