Answer
11.2 years
Work Step by Step
Insert the given values for A, P, n, r into the formula.
Solve for t.
$15,000=7250(1+\displaystyle \frac{0.065}{12})^{12t}\qquad.../\div 7250$
$\displaystyle \frac{15,000}{7250} =(1+\frac{0.065}{12})^{12t}$
$\displaystyle \frac{60}{29}=(1+\frac{0.065}{12})^{12t}\qquad .../$apply ln() to both sides..
$\displaystyle \ln(\frac{60}{29})=12t\cdot \mathrm{l}\mathrm{n}(1+\frac{0.065}{12}) \displaystyle \qquad .../\div 12\mathrm{l}\mathrm{n}(1+\frac{0.065}{12})$
$ t=\displaystyle \frac{\ln(\frac{60}{29})}{12\mathrm{l}\mathrm{n}(1+\frac{0.065}{12}) }\approx$11.2156315338$\approx 11.2$ years
