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