$3.$ Suppose a hedge fund earns $1\%$ per month every month. $(4$ points$)$

a$.$ What is the EAR on an investment in this fund?

b$.$ If you need $$1$ million dollars in $5$ years, how much do you have to invest in the fund today?

c$.$ If you invest $$1$ million today, how much money will you have in $5$ years?

d$.$ If you invest $$1,000$ every month for $24$ months, starting immediately $($i$.$e$.,$ first investment at time $0,$ last investment $23$ months from now$),$ how much will you have at the end of $2$ years?

e$.$ If you need $$1$ million dollars in $5$ years, and you are going to invest the same amount every month for $24$ months, starting immediately $($i$.$e$.,$ just like part $($d$)$ above$)$ how much do you have to invest?

f$.$ If you invest today, how long will it take to triple your money?