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In how many years will a sum of Rs. 800 at 10% per annum compounded semi annually become Rs. 926.10?

a) $$1\frac{1}{3}$$ years
b) $$1\frac{1}{2}$$ years
c) $$2\frac{1}{3}$$ years
d) $$2\frac{1}{2}$$ years

Answer: b
Explanation:
$$\eqalign{ & {\text{Let the time be }}n{\text{ year}} \cr & {\text{800}} \times {\left( {1 + \frac{5}{{100}}} \right)^{2n}} = 926.10 \cr & {\left( {1 + \frac{5}{{100}}} \right)^{2n}} = \frac{{9261}}{{8000}} \cr & {\left( {\frac{{21}}{{20}}} \right)^{2n}} = {\left( {\frac{{21}}{{20}}} \right)^3} \cr & 2n = 3 \cr & n = \frac{3}{2} \cr & n = 1\frac{1}{2}{\text{years}} \cr} $$

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