A technical company intends to upgrade its equipment in view of some projects it has undertaken to implement and wishes to receive a loan of 150,000. The annual interest rate of the loan is variable and specifically 9% for the first half of the repayment period and 15% for the next half of the period. Based on the expected future income from the projects, the shareholders of the company plan a loan repayment installment plan that includes amount A each installment in the first third of the loan term, 2A each installment in the second third and 3A each installment in the last part of the repayment period. Repayment installments start with the first period and are paid in all cases at the end of the period.

(a) If the term of the loan is 30 years and the repayment installments are annual, calculate the installments in the three repayment periods of the loan. What is the cumulative amount of the installments that the company will pay (in relation to the loan amount)?

(b) With the basic repayment scenario (A-2A-3A) for the three repayment periods, if the basic installment of loan A is 11,500, calculate the repayment period of the loan. This period will be divided into three subperiods of the same duration to which the three installment levels apply. The period will also be divided into two subperiods of the same duration to which the two given interest rates apply. The result in the general case will be decimal but this is acceptable.