Answer:
In 3.5 years she will pay the wardrobe
Explanation:
We are going to calculate the time for an annuity of 270 with monthly compound interest to achieve 8368 present value
[tex]C * \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
We post the know values
[tex]270 * \frac{1-(1+.18/12)^{-time*12} }{.18/12} = 8,368\\[/tex]
First: we clear the dividend
[tex]1-(1+.015)^{-time*12} = 8,368\times \frac{(0.18/12)}{270}\\[/tex]
Then we set up the formula to use logarithmic
[tex]1.015^{-time*12} = 1-.464888888888\\log_{1.015} \: 0.5351111111 = -time*12[/tex]
We use logarithmic properties to solve for time
[tex]\frac{log 0.535111111}{log 1.015} = -41.99725593 = -42[/tex]
-42 = time * -12
-42/-12 = 3.5 = time
It will take 42 months or 3.5 years
