Question

If the interest is compounded half yearly , calculate the amount when the principal is Rs.8000,the rate of interest is 10%p.a and the duration is one year. *
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Answer 1

Given:

• Principal = Rs. 8000
• Time = 1 year
• Rate = 10 %

What To Find:

We have to -

• Find the amount if the interest is compounded half-yearly.

Formula Needed:

$\bf A = P \bigg(1+\dfrac{R}{200} \bigg)^{2T}$

Where -

• A = Amount
• P = Principal
• R = Rate
• T = Time

Solution:

Using the formula,

$\sf \to A = P \bigg(1+\dfrac{R}{200} \bigg)^{2T}$

Substitute the values,

$\sf \to A = 8000 \bigg(1+\dfrac{10}{200} \bigg)^{2 \times 1}$

Solve the powers,

$\sf \to A = 8000 \bigg(1+\dfrac{10}{200} \bigg)^{2}$

Solve the brackets,

$\sf \to A = 8000 \bigg(\dfrac{210}{200} \bigg)^{2}$

Remove the brackets,

$\sf \to A = 8000 \times \dfrac{210}{200} \times \dfrac{210}{200}$

Cancel the zeros,

$\sf \to A = 8 \times \dfrac{210}{2} \times \dfrac{21}{2}$

Multiply 8, 210 and 21,

$\sf \to A = \dfrac{35280}{2 \times 2}$

Multiply 2 with 2,

$\sf \to A = \dfrac{35280}{4}$

Divide 35280 by 2,

$\sf \to A = 8820$

Final Answer:

∴ Thus, the amount is Rs. 8820.