Question

The population of a town is increasing at a rate of 2.8% per year. In 2001 the town had a population of 34,229. Find the population of the town in 2013

Answer 1

The population of the town in 2013 is 47,677. (to the nearest whole number)

Explanation:

To calculate this, we will compare the increase to the increase of the present value of an amount of money invested in 2001, increasing at an annual percentage rate of 2.8%, to yield the future value worth a certain amount in 2013. To calculate, the formula below is used:

FV =
`PV ( 1 + (i)/(n)) ^(n*t)`

where:

FV = Future Value = ???

PV = present value = 34,229

i = interest in decimal = 2.8% = 0.028

n = frequency of compounding period per year = 1

t = number of compounding years = 2001 to 2013 = 12 years.

FV =
`34,229(1+(0.028)/(1) )^((1*12))`

FV = 34,229 × (1.028)¹²

FV = 47,677.29 = 47,677 (to the nearest whole number)