Let us now see how the logistic regression model can be used to identify loans that are expected to be profitable.

(i) If the loan is paid back in full, then the investor makes interest on the loan. However, if the loan is not paid back, the investor loses the money invested. Therefore, the investor should seek loans that best balance this risk and reward. To compute interest revenue, consider a $c investment in a loan that has an annual interest rate r over a period of t years. Using continuous compounding of interest, this investment pays back c × e^(rt) dollars by the end of the t years. How much does a $10 investment with an annual interest rate of 6% pay back after 3 years, using continuous compounding of interest?

(ii) While the investment has this value after collecting interest, the investor had to pay c dollars for the investment. What is the profit to the investor if the investment is paid back in full? What is the profit to the investor if the investment is not paid back in full?

(iii) Compute the profit of $1 investment in each loan, and save your result to a variable named Profit. Keep in mind that the profit computation should depend on the value of the variable NotFullyPaid. What is the maximum profit of a $1 investment in any loan in the test set?