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

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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