An investor invests $$106,000$ in a managed fund at the beginning of Year $1.$ Over the course of the first year the value of the fund increases by

$$21101.$ At the end of Year $1,$ the investor invests another $$47,000.$ Over the course of the second year the value of the fund falls by $$16645.$ At the

end of Year $2$ the investor invests another $$50,000.$ At the end of Year $3$ the value of the fund has increased to $$258378,$ which the investor then

withdraws.

What is the annual rate of return from this investment the point of view of the portfolio manager?

a$.8\%$

b$.11\%$

c$.9\%$

d$.12\%$