3. 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. 3. 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