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Question
Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly.
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Solution
Let the rate percent per annum be R.
Because interest is compounded every six months, n will be 3 for 1.5 years.
Now,
\[A = P \left( 1 + \frac{R}{200} \right)^n \]
\[2, 315 . 25 = 2, 000 \left( 1 + \frac{R}{200} \right)^3 \]
\[ \left( 1 + \frac{R}{200} \right)^3 = \frac{2, 315 . 25}{2, 000}\]
\[ \left( 1 + \frac{R}{200} \right)^3 = 1 . 157625\]
\[ \left( 1 + \frac{R}{200} \right)^3 = \left( 1 . 05 \right)^3 \]
\[1 + \frac{R}{200} = 1 . 05\]
\[\frac{R}{200} = 0 . 05\]
\[ = 10\]
Thus, the required rate is 10 % per annum.
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