Answer:
The approximate monthly rate of growth is 1.24%
Step-by-step explanation:
we have the future value formula
[tex]F=P(1+r)^t[/tex]
we have
[tex]r=16\%=16/100=0.16[/tex] ----> annual interest rate
so
[tex]F=P(1+0.16)^t[/tex]
[tex]F=P(1.16)^t[/tex]
Find the approximate monthly rate of growth
Remember that
[tex]1\ year=12\ months[/tex]
so
Divide the number of periods t by 12
[tex]F=P(1.16)^{\frac{t}{12}}[/tex]
Applying power rules property
[tex]F=P(1.16^\frac{1}{12})^t[/tex]
[tex]F=P(1.0124)^t}[/tex]
[tex]1.0124-1=0.0124[/tex]
Convert to percentage
[tex]0.0124*100=1.24\%[/tex]
therefore
The approximate monthly rate of growth is 1.24%
