4. The housing board of a newly planned town anticipates that over the next 12 y

Question

4. The housing board of a newly planned town anticipates that over the next 12 years, 7,000 new residents will move in each year. In addition to the effect of new residents moving in, the board anticipates that each year the town’s population (i.e. whoever has been living there for the entirety of that year) will grow at an annual rate of 1.5%, due to the ordinary population changes resulting from births and deaths. Assume that whenever new residents move in they do so at the end of the year, and don’t start reproducing until the following year.

4a. Why can this population growth scenario be considered an ordinary annuity?

4b. What will the population be at the end of 12 years of such growth?

4c. What if the town actually started out at the beginning of year 1 with 500,000 residents? What would be the population at the end of 12 years?

Explanation / Answer

4a. The scenario involves addition of fixed no. of residents at the end of each year just like the case of ordinary annuity.

4b. Population at the end of 12 years = Annual addition of new residents * [(1+annual growth rate)12 - 1] / annual growth

= 7,000 * [(1+1.5%)12 - 1] / 1.5%

= 91,288.48 ~ 91,289

4c. Population at the end of 12 years with 500,000 residents at the begining of year 1 = 7,000 * [(1+1.5%)12 - 1] / 1.5% + 500,000 * (1+1.5%)12

= 689,097.57 ~ 689,098

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