Answer
8.2 years
Work Step by Step
Insert the given values for A, P, n, r into the formula.
Solve for t.
$20, 000=12,500(1+\displaystyle \frac{0.0575}{4})^{4t}\qquad.../\div 12, 500$
$1.6=(1.014375)^{4t}\qquad .../$apply ln() to both sides..
$\ln 1.6=4t \mathrm{l}\mathrm{n}(1.014375) \qquad .../\div 4\mathrm{l}\mathrm{n}(1.014375)$
$ t=\displaystyle \frac{\ln 1.6}{4\ln \mathrm{l}.014375}\approx$8.23258686072$\approx 8.2$ (years)
