Answer:
The required inequality is [tex]27000\leq 20000(1+0.08)^n[/tex].
Step-by-step explanation:
The principle amount is $20,000.
The interest rate is 8% per year.
The formula of compound interest annually is
[tex]A=P_0(1+r)^n[/tex]
Where, P₀ is principle amount, r is rate and n is time in years.
The amount is
[tex]A=20000(1+0.08)^n[/tex]
We need the amount at least $27,000. It means $27000 or more than $27,000.
[tex]27000\leq 20000(1+0.08)^n[/tex]
[tex]27\leq 20(1+0.08)^n[/tex]
[tex]n\geq 3.899[/tex]
Therefore the required inequality is [tex]27000\leq 20000(1+0.08)^n[/tex].
