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Question
In what time will Rs 4400 become Rs 4576 at 8% per annum interest compounded half-yearly?
Solution
Let the time period be n years.
R = 8 % = 4 % (Half - yearly)
Thus, we have:
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
\[4, 576 = 4, 400 \left( 1 + \frac{4}{100} \right)^n \]
\[4, 576 = 4, 400 \left( 1 . 04 \right)^n \]
\[ \left( 1 . 04 \right)^n = \frac{4, 576}{4, 000}\]
\[ \left( 1 . 04 \right)^n = 1 . 04\]
\[ \left( 1 . 04 \right)^n = 1 . {04}^1 \]
On comparing both the sides, we get:
n = 1
Thus, the required time is half a year.
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