In what time will $R s 5000$ become $R s 5408$ at $8 % p . a .$ compounded half yearly $?$

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Solution

Given Rate of interest is $r = 8 % = 0.08$
Principal Amount is $A = 5, 000$
Time is $t$ years
Interest is compounded yearly twice $⟹ n = 2$
Amount $= P (1 + \frac{r}{n})^{n t} = 5000 \times (1 + \frac{0.08}{2})^{2 t} = 5, 408$
$(1.0816)^{t} = \frac{5408}{5000} = 1.0816 ⟹ t = 1$

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