Answer:
It will be after 462 months
Explanation:
We use the annuity formula for present value
[tex]C * \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
We post our know values and start solving for time:
[tex]1000 * \frac{1-(1+0.005)^{-time} }{0.005} = 180,000[/tex]
First we clear the dividend:
[tex]1-(1+0.005)^{-time} = 180,000/1000\times 0.005[/tex]
Then we clear for the power
[tex](1.005)^{-time} = 1-0.9[/tex]
We set up the formula using logarithmic
[tex]log_{1.005}\: 0.1 = -time[/tex]
And use logarithmic properties to solve for time:
[tex]\frac{log\:0.1}{log\:1.005} = -time[/tex]
[tex]-461.6673541 = -time[/tex]
time 462 months
