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Finding CI When Rate Compounded Anually or Semi - Anually

In how many y...

Question

In how many years will $R s . 7200$ to $R s . 7938$ at $10 %$ per annum when compounded half-yearly.

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Solution

The correct option is B: $1$ year
Principal, $P = R s 7200$
Amount, $A = R s . 7938$
Rate, $r = 10 %$ per annum
Time, $t = ?$
When interest is compounded half- yearly
Rate @ half yearly $= \frac{10}{2}$
$n =$ number of times interest added $=$ number of half year
Amount, $A = P (1 + \frac{r}{100})^{n}$
$7938 = 7200 (1 + \frac{5}{100})^{n}$
$\Rightarrow \frac{7938}{7200} = (1 + 0.05)^{n}$
$\Rightarrow \frac{3969}{3600} = (\frac{105}{100})^{n}$
$\Rightarrow \frac{1323}{1200} = (\frac{105}{100})^{n}$
$\Rightarrow \frac{441}{400} = (\frac{105}{100})^{n}$
$\Rightarrow (\frac{21}{20})^{2} = (\frac{21}{20})^{n}$
$∴ n = 2$
when $n =$ number of half year $= 2,$ time will be $1$ complete year.

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