The population of a new city is $5$ million and is growing at $20\%$ annually. How many years would it take to double at this growth rate?
This can also be solved very easily by using the rule of 72 (http://www.investopedia.com/ask/answers/04/040104.asp) the time taken by a quantity to get doubled at a constant growth rate is $72/rate$. so for this case answer is $72/20 = 3.6$.
FV = PV × (1+r)n
where FV = Future Value
PV = Present Value
r = annual interest rate
n = number of periods
Let us suppose the initial population is $100$
Ans Should be A) 3-4 yr
initial population was 5 million
growing rate = 20 % per annum
now after end of 1 yr population will be = 5(1+20/100) = 6million , ( A= p(1+r/100)$^T$ )
after end of 2nd yr population will be = 6(120/100) = 72/10= 7.2 million
after end of 3rd year population will be = 7.2(120/100)= 43.2/5 = 8.65 million
after end of 4th year population will be = 8.65(120/100) = 10 .38 million ..which is required so it should be option A)