If an investment declines by 20 each year in an exponential
If an investment declines by 20% each year in an exponential pattern, by how much does it change over two years? Question options:
A) the value after two years is 0.6 times as large as the starting value
B) the value after two years is (0.2)(2) times as large as the starting value
C) –36%
D) -40%
Solution
let the value of the investment after t year is
P=P0(1-r)^t which is exponential
here, r=20%=0.2
t=2 year
so, P=P0(1-0.2)^2=P0(0.8)^2=0.64Po
so, change in values=final - initial=0.64P0 - 1P0= -0.36 P0
so, % change is= - 36%........(c)ans

