Answer
$7.3$ years
Work Step by Step
The formula for compound interest with $ n $ compoundings per year is given by : $ A= P(1+\dfrac{r}{n} )^{nt}$
Plug in the given data.
$20,000=12,500 (1+\dfrac{0.065}{4} )^{4t}$
or, $1.6 =(1+0.016)^{4t}$
or, $1.6=(1.016)^{4t}$
Take log base 1.016 of each side.
$\log_{1.016} 1.6=4t \implies t=7.3$ years
