Question $3(20$ pts$)$ Your friend is $40$ years and wishes to retire at $65.$ She wants

to pick your finance brains. She wants to know which of the following options will

allow her to have more money when she retires. Option $1$ is to invest $$10,000$ per

year for thirteen years, and then leave it untouched for $12$ years until she retires.

Option $2$ is to deposit $$6,000$ at the end of each year into an investment for $25$

years until she retires. Both accounts earn $7\mathrm{.}5\%$ per year. Please calculate the

retirement money saved in each option. Show all your calculations. State which

option is better and by how much.