You can only choose one of the three investment options below. Calculate the annual rate of return of

each option and choose the one with the highest annual rate of return. $[15$ points$]$

a$.$ One$-$time $$50,000$ investment today and receive a one$-$time amount of $$220,000$ in $11$

years.

b$.$ Invest $$5,000$ today and $$6,300$ at the end of each year for $11$ years. You will receive a

one$-$time amount of $$178,000$ at the end of year $11.$

c$.$ Invest $$5,300$ every year for $11$ years starting today. You will receive a one$-$time amount

of $$140,360$ at the end of year $11.$

You want to buy a house within $5$ years, and you are currently saving for the down payment. You plan to save $$3,000,$ $$3,500,$ $$4,050,$ $$4,300$ and $$4,655$ at the end of each year. Your expected annual return of your savings each year is $7\%.$ How much will you have for the down payment at the end of Year $5?$