Answer:
After 48 months the value will increase by 10 percent of the initial value.
Step-by-step explanation:
Let's first find the rate of increase for each period which is 3 months here.
According to the table at month [tex]x=0[/tex] value is [tex]2000[/tex]dollars and at month [tex]x=3[/tex] value is [tex]2012[/tex]dollars.
∴[tex]2012=2000(1+\frac{r}{100} )^1[/tex]
⇒[tex]1+\frac{r}{100} =\frac{2012}{2000}=1.006[/tex]
⇒[tex]r=0.006*100[/tex]
⇒[tex]r=0.6[/tex]%
Now the question is to find how long it will take for the investment value to increase 10 percent.
[tex]y=2000(1+0.006)^\frac{x}{3}[/tex]
[tex]2000(1+0.1)=2000(1.006)^\frac{x}{3}[/tex]
⇒[tex](1.006)^\frac{x}{3} =1.1[/tex]
⇒[tex]\frac{x}{3}=\frac{log(1.1)}{log(1.006)}[/tex]
⇒[tex]x=3(\frac{log(1.1)}{log(1.006)} )[/tex]
⇒[tex]x=47.7979126....[/tex]
∴at [tex]x=48[/tex] the value will slightly cross 10 percent increase.
