Question

You buy Apple stock for $120 per share over a period of time the stock value increased at a weekly rate of 5% you sell the stock for $180 per share about how many weeks did you on the stock for

Answer 1

8.31 weeks

Explanation:

Given that the cost of one share of Apple stock, C=$120

Rate is the increment of the stock value, R= 5%/week=0.05 / week.

Assuming that after t week, the stock has been sold for $180.

Since the stock value increased at 5% every week, so, the interest is compounded weekly, so

`S=C\left(1+R\right)^t \\\\ \Rightarrow 180 = 120\left(1+0.05\right)^t \\\\ \Rightarrow 180 = 120\left(1.05 )^t \\\\`

`\Rightarrow (180)/(120)=1.05^t \\\\\Rightarrow 1.5=1.05^t`

`\Rightarrow \ln(1.5)=t \ln(1.05)` [taking log both sides]

`\Rightarrow t=\frac {\ln(1.5)}{\ln(1.05)}=8.31` weeks

Hence, after 8.31 weeks the stock has been sold for $180.