An investment has a cost of $$7500.$ The investment will have a payout of $x$ at the end of the first year. This initial payout $x$ will grow at the rate of $10\%$ per year for the next $2$ years, then by $7\%$ per year for the next $4$ years, then by $4\%$ for the next $3$ years, and then at the rate of $3\%$ per year for the following $5$ years. You believe the riskiness of this investment is $8\%.$

CHAPTER $1$

EXERCISE $3$

a$.$ Calculate the smallest $x$ that would entice you to invest.