Question

The population of a village increases at the rate of 5% p.a. If its present population is 18,000
what will be the population of the village after 2 years?​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Population increases at 5% per year.

• Present population is 18000.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Population of village after 2yrs.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Present population is 18000.

Next year population will be increased by 5%

$\\ \sf \: population = 18000 + 5\% \: of \: 18000 \\ \\ \sf \: population = 18000 + \frac{5}{100} (18000) \\ \\ \sf \: population = 18000 + 5(180) \\ \\ \sf \: population = 18000 + 900 \\ \\ \sf \: \therefore \: \pink{population \: after \: 1 \: yr \: is \: 18900.}$

Again , for next year , population will increase by 5%.

$\\ \sf \: population = 18900 + 5\% \: of \: 18900 \\ \\ \sf \: population = 18900 + \frac{5}{100} (18900) \\ \\ \sf \: population = 18900 + 5(189) \\ \\ \sf \: population = 18900 + 945 \\ \\ \small \sf \: \therefore \: \pink{population \: after \: two \: yrs \: will \: be \:19845. }$

Answer 2

present population is 18000

population after 2 years=

p(1+r/100)^n = 18000(1+5/100)^2

you can see this in the photo