You have just been elected into the "Society of Honerable 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?