Question : In how many years will a sum of Rs. 800 at 10% per annum compounded semi-annually become Rs. 926.10?
Option 1: $2\frac{1}{2}$ years
Option 2: $3$ years
Option 3: $2$ years
Option 4: $1\frac{1}{2}$ years
Correct Answer: $1\frac{1}{2}$ years
Solution :
Given:
Rate = $\frac{10}{2}$= 5% per half year.
Let time = $n$, number of half years = $2n$.
Then, $800×(1+\frac{5}{100})^{2n}=926.10$
⇒ $(\frac{21}{20})^{2n}=\frac{9261}{8000}=(\frac{21}{20})^{3}$
⇒ $2n=3$
⇒ $n=\frac{3}{2}=1\frac{1}{2}$ years
Hence, the correct answer is $1\frac{1}{2}$ years.
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