Question : The population of a certain village increases by 5% annually. Its present population is 8200. After two years the population will be (approximately):
Option 1: 9200
Option 2: 9246
Option 3: 9040
Option 4: 9161
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Correct Answer: 9040
Solution :
Present population, $P$ = 8200
Time, $t$ = 2 years
Rate, $r$ = 5%
Population after $t$ years at the rate of $r$ %
= $P(1+\frac{r}{100})^{t}$
= $8200(1+\frac{5}{100})^{2}$
= $8200(\frac{21}{20})^{2}$
= $8200×\frac{441}{400}$
= $9040.5\approx 9040$
Hence, the correct answer is 9040.
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