Answer:
[tex]t=4\ years[/tex]
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=?\ years\\ P=\$5,000\\ A=\$6,000\\r=5\%=5/100=0.05[/tex]
substitute in the formula above
[tex]6,000=5,000(1+0.05t)[/tex]
solve for t
Simplify
Divide by 5,000 both sides
[tex]1.2=1+0.05t[/tex]
subtract 1 both sides
[tex]0.05t=1.2-1[/tex]
[tex]0.05t=0.2[/tex]
divide by 0.05 both sides
[tex]t=4\ years[/tex]
