# How do you use the formula to solve these problems: Initial deposit of $1000, annual rate of 8.5% and final value is$1800?

Feb 9, 2016

Final Value $= \left(\text{Initial Value}\right) \times {\left(1 + i\right)}^{t}$

#### Explanation:

Using the formula ...

Final Value $= \left(\text{Initial Value}\right) \times {\left(1 + i\right)}^{t}$

$1800 = \left(1000\right) {\left(1 + 0.085\right)}^{t}$

Simplify ...

${\left(1.085\right)}^{t} = 1.8$

Now take the log of both sides ...

$\log {\left(1.085\right)}^{t} = \log 1.8$

$t \log \left(1.085\right) = \log 1.8$

$t = \frac{\log 1.8}{\log 1.085} \approx 7.2$ years

hope that helped