You have just been elected into the $$Society of Honorable Engineers.$$ First$-$year dues are waived in honor of your election. Thus, your first$-$payment of $$200$ is due at the end of the year, and annual dues are expected to increase $3\%$ annually. After $40$ years of paying dues you become a life member and pay no more dues. Instead of paying annual dues, however, you can pay a one$-$time $$2000$ life membership fee.

$($a$)$ Show the equation for determining the rate of return for buying a life membership.

$($b$)$ What is the rate of return?

using excel for b