Answer
$8.2$
Work Step by Step
Solve the given formula for $ t.$
$ A=P(1+\displaystyle \frac{r}{n})^{nt}\quad $ ... $/\div P $
$(A/P)=(1+\displaystyle \frac{r}{n})^{nt}\quad $ ... $/\ln(...)$
$\displaystyle \ln(A/P)=nt\ln(1+\frac{r}{n})\quad $ ... $/\displaystyle \times\frac{1}{n\ln(1+\frac{r}{n})}$
$ t=\displaystyle \frac{\ln(A/P)}{n\ln(1+\frac{r}{n})}$
Insert $ P=12,500, \ n=4, \ r=0.0575, \ A=20,000$
$ t=\displaystyle \frac{\ln(20,000/12,500)}{4\cdot\ln(1+\frac{0.0575}{4})} \approx 8.233$ (round to 1 dec. place)
