Suppose that the investor of problem 14 bought 100 shares of the Geo
Fund at $70 per share and that, for the sake of simplicity, we only consider the returns the fund earns and automatically reinvests at the rate of 2% per month. Find
a. the beginning value of the fund.
To find the beginning value of the fund, we need to calculate the value of the investment at the start.
Step 1: Calculate the value of each share after one month.
The rate of reinvestment is 2% per month. So, the value of each share after one month will be increased by 2% of its current value.
The new value of each share after one month can be calculated as follows:
New value = Current value + (Current value * 0.02)
Step 2: Calculate the value of the investment after one month.
The investor bought 100 shares at $70 per share, so the initial investment was $70 * 100 = $7000.
After one month, the value of each share will increase by 2%, i.e., $70 * 0.02 = $1.40.
So, the new value of each share after one month will be $70 + $1.40 = $71.40.
The value of the investment after one month can be calculated as follows:
New investment value = Number of shares * New value of each share
= 100 * $71.40
= $7,140
Therefore, the beginning value of the fund is $7,140.