Question 1010383
the general formula for continuous compounding is:


A = p * e^(rt)


A is the future value
p is the present value
r is the continuous compounding growth rate per time period.
t is the numbe of time periods.


the time periods for this problem are expressed in years.


the country with the highest value of r has the highest continuous compounding growth rate.


that country would be iraq with a continuous compounding growth rate of .027 per year.


to convert from continuous compounding growth rate to annual compounding growth rate, use the following formula.


(1+ar) = e^cr


when cr = .027, that formula becomes:


(1+ar) = e^.027 = 1.027367803


to solve for ar, subtract 1 from both sides of the equation to get:


ar = .027367803.


that's the annual compounding growth rate.


the annual compounding growth rate percent is equal to 2.7367803%.


the population in iraq is growing at a rate of 2.7367803% per year.


since the formulas are equivalent, they should yield the same result.


using continuous compounding formula for 1 year:


26.8 * e^.027 = 27.53345711


using annual compounding formula for 1 year:


26.8 * (1.027367803) = 27.53345711


they're the same, confirming that the two formulas are equivalent.


the annual growth rate for all of the countries is shown below:


india:
e^.014 = 1.014098459 - 1 = .014098459 = 1.4098459%
iraq:
e^.027 = 1.027367803 - 1 = .027367803 = 2.7367805%
japan:
e^.001 = 1.0010005 - 1 = .0010005 = 1.0005%
russia:
e^-.004 = .9960079893 - 1 = -.0039920107 = -.39920107%