## Precalculus (6th Edition) Blitzer

$7.3$ years
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