Answer:
The inequality that represent this situation is [tex]10,000(1+0.05n) \geq 15,000[/tex]
The minimum number of years is 10
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=n\ years\\ P=\$10,000\\A\geq \$15,000\\r=5\%=5/100=0.05[/tex]
substitute in the formula above
[tex]10,000(1+0.05n) \geq 15,000[/tex]
Solve for n
[tex](1+0.05n) \geq 1.5[/tex]
[tex]0.05n \geq 1.5-1[/tex]
[tex]0.05n \geq 0.5[/tex]
[tex]n \geq 10[/tex]
therefore
The minimum number of years is 10
