Question

14. Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1
years, interest being compounded half-yearly? Please answer it fast....... ​

Answer 1

Question :

Find the rate percent per annum if Rs 2000 amount to Rs 2662 in 3/2 years, interest being compounded half-yearly?

Solution :

$\rule {193}{1}$

$\underline{\bold{Given:}}$

• Amount = Rs 2662
• Principal = Rs 2000
• Time = 3/2 years

$\underline{\bold{To\:Find :}}$

The rate percent per annum.

$\rule {193}{1}$

Let rate be x.

We convert rate into half :

$\implies Rate = \frac{x}{2}$

We convert time in half years to find compound interest half-yearly :

$\implies Time = (\frac{3}{2} \times 2) \: half-years\\ \implies Time = 3 \: half-years$

Now we have :

• Amount = Rs 2662
• Principal = Rs 2000
• Time = 3 half- years

$\boxed{\purple{A= P( {1 + \frac{R}{100} })^{T} }}$

$\implies A= P( {1 + \frac{R}{100} })^{T} \\ \implies 2662 = 2000{(1 + \frac{x}{200} )}^{3} \\ \implies \frac{2662}{2000} =( {1 + \frac{x}{200} })^{3} \\ \implies \frac{1331}{1000} = ( {1 + \frac{x}{200} })^{3} \\ \implies {( \frac{11}{10} )}^{3} = ( {1 + \frac{x}{200} })^{3} \\ \implies \frac{11}{10} = 1 + \frac{x}{200} \\ \implies \frac{11}{10} = \frac{200+ x}{200} \\ \implies 11 \times 200 = 10(200 + x) \\ \implies 2200 = 2000 + 10x\\ \implies 2200 - 2000 = 10x\\ \implies 200 = 10x \\ \implies \frac{200}{10} = x\\\implies 20\% = x \\\implies x= 20\%$

$\boxed{\green{\therefore {Rate= 20\%}}}$

Answer 2

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