In what time 8000 RS will amount to 9261 rs at 10% per annum compound interest when the interest is compounded half yearly?

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1. In what time ₹ 8,000 will amount to ₹ 9,261 at 10% per annum compound interest, when the interest is compounded half yearly ?

1. 4. 2 years

Interest is compounded half yearly.Given that , P = ₹ 8000 , A = ₹ 9261 , Rate of interest = 5%

Let Time =	n	years or n half-years
2

Using the given formula ,

A = P		1 +	R		T
100

⇒  9261 = 8000		1 +	5		n
100

⇒	9261	=		21		n
8000	20

⇒		21		3	=		21		n
20		20

⇒  n = 3 half years =	3	years = 1	1	years
2	2

Q. In what time 8000 Rs. will amount to 9261 Rs. at 10% per annum compound interest, when the interest is compounded half yearly?
Answer: [A] 1.5 years
Notes: Interest is compounded half yearly. ∴ Rate of interest = 5% $latex Time = \frac{n}{2}\ years&s=1$ $latex \because A = P(1 + \frac{R}{100})^{T}&s=1$ $latex => 9261 = 8000 (1 + \frac{5}{100})^{n}&s=1$ $latex => \frac{9261}{8000} = (\frac{21}{20})^{n}&s=1$ $latex => (\frac{21}{20})^{3} = (\frac{21}{20})^{n}&s=1$ $latex => n = 3\ half\ years$ $latex = \frac{3}{2}\ years = 1\frac{1}{2}\ years&s=1$ Hence option [A] is correct answer.

Q. In what time 8000 Rs. will amount to 9261 Rs. at 10% per annum compound interest, when the interest is compounded half yearly?
Answer: [A] 1.5 years
Notes: Interest is compounded half yearly. ∴ Rate of interest = 5% $ Time = \frac{n}{2}\ years$ $ \because A = P(1 + \frac{R}{100})^{T}$ $ => 9261 = 8000 (1 + \frac{5}{100})^{n}$ $ => \frac{9261}{8000} = (\frac{21}{20})^{n}$ $ => (\frac{21}{20})^{3} = (\frac{21}{20})^{n}$ $ => n = 3\ half\ years$ $ = \frac{3}{2}\ years = 1\frac{1}{2}\ years$ Hence option [A] is correct answer.