When principal P is compounded semi-annually at r % per annum for t years, then Amount = _________
Solution:
When principal P is compounded semi-annually at r % per annum for t years, then
\(Amount =P(1 + \frac{r/2}{100})^{2t}\)
✦ Try This: What will be the amount at the end of the year if a sum of Rs. 12000 is compounded semiannually at the annual rate of interest 12%.
Since the interest is compounded semiannually, the applicable rate of interest will be r/2
And the conversion period will be 2t where t = number of years. The basic equation will be:
Amount = \(P(1 + \frac{r/2}{100})^{2t}\)
P = 120000 and t = 1 and r = 12%
Amount = \(12000(1 + \frac{12/2}{100})^{2(1)}\)
= \(12000(1 + \frac{6}{100})^{2}\)
= 12000(1 + 6/100)2
= 12000(1.1236)
= 13483.20
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 8
NCERT Exemplar Class 8 Maths Chapter 9 Problem 32
When principal P is compounded semi-annually at r % per annum for t years, then Amount = _________
Summary:
When principal P is compounded semi-annually at r % per annum for t years, then \(Amount = P(1 + \frac{r/2}{100})^{2t}\)
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