$7\mathrm{.}13$ An investor bought $100$ shares of stock at a cost of $$10$ per

share. He held the stock for $15$ years and then sold it for a

total of $$4,000.$ For the first three years, he received no

dividends. For each of the next seven years, he received total

dividends of $$50$ per year. For the remaining period, he

received total dividends of $$100$ per year. What rate of

return did he make on the investment?