Todd and Diane plan to take out a mortgage from Humorous Money Company to purchase a home. The current fixed-interest rate on a 30-year loan is 8%. For no additional service charge Humorous Money will...

Todd and Diane plan to take out a mortgage from Humorous Money Company to purchase a home. The current fixed-interest rate on a 30-year loan is 8%. For no additional service charge Humorous Money will allow Todd and Diane to “lock in” the current rate of 8% (option 1). For a service charge of $50 they can take whatever the current rate happens to be in 4 weeks (option 2). For a service charge of $100 Humorous Money will let the rate drift for 4 weeks but lock it in if it hits 8.2% or 7.8% (option 3). The sales agent says that option 3 protects Todd and Diane from getting stuck with a very high rate while giving them a chance for a lower rate. Interest rates can change weekly, and Diane believes that interest rates are more likely to go down than up. For the next 4 weeks she believes that the following model is a good representation of how the interest rate will change each week: The rate will go up 0.1% with probability 0.3, go down 0.1% with probability 0.4, and stay the same with probability 0.3. Under this model, help Todd and Diane decide which option is best for them.