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The population of a city grows at the annual rate of \(3 \%\). What percentage increase is expected in \(5 \mathrm{yr}\) ?
Options:
Solution:
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Verified Answer
The correct answer is:
\(15.9 \%\)
Let the population in begining is \(P_0\), then according to the question percentage increase in 5 yr expected is
\(\begin{aligned}
\frac{P_0\left(1+\frac{3}{100}\right)^5-P_0}{P_0} \times 100 & =\left[\left(\frac{103}{100}\right)^5-1\right] \times 100 \\
& =\left[(1.03)^5-1\right] \times 100 \\
& =[1.159-1] \times 100=15.9 \%
\end{aligned}\)
Hence, option (d) is correct.
\(\begin{aligned}
\frac{P_0\left(1+\frac{3}{100}\right)^5-P_0}{P_0} \times 100 & =\left[\left(\frac{103}{100}\right)^5-1\right] \times 100 \\
& =\left[(1.03)^5-1\right] \times 100 \\
& =[1.159-1] \times 100=15.9 \%
\end{aligned}\)
Hence, option (d) is correct.
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