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=\$3,900\\ A=\$10,000\\r=0.0783[/tex]
substitute in the formula above
[tex]10,000=3,900(1+0.0783t)[/tex]
Solve for t
[tex]10,000/3,900=(1+0.0783t)[/tex]
[tex](10,000/3,900)-1=0.0783t[/tex]
[tex]0.0783t=1.5641[/tex]
[tex]t=1.5641/0.0783[/tex]
[tex]t=19.98\ years[/tex]
therefore
the answer is the option C
[tex]20\ years[/tex]
