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 with a (real) annual interest rate of 12%. Based on the expected future income from the projects, the shareholders of the company plan a loan repayment installment plan that includes installments of amount A each in the first third of the loan term, amount 2A each installment in the second third and amount 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. Answer the following independent questions by recording the calculation relationships in each case. Compare the results of each query with those of related queries and comment (justify) the differences.

(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 sum of the installments that the company will pay?

(b) Repeat the solution of question (a) but considering a reverse repayment order, i.e. 3A at the beginning, 2A afterwards and A at the last repayment period. Compare the results of cases (a) and (b) and justify the differences.

(c) With the basic repayment scenario (A-2A-3A) for the three repayment periods, if the basic installment of loan A is 14,153, 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 result in the general case will be decimal but this is acceptable. Compare the results of cases (a) and (c) and justify the differences.

(d) On the basis of question (a), if the basic installment A is 10,000, calculate the interest rate of the loan. Compare the results of cases (a) and (d) and justify the differences.

(e) On the basis of question (a), calculate the amount of the loan that has not been repaid at the end of year 20 and after the payment of the respective installment has preceded.

(f) Based on question (a) as to the repayment period, if the installments are monthly, the effective annual interest rate remains at 12% and the loan is repaid if the monthly installments are calculated in its three repayment periods. loan. Compare the results of cases (a) and (f) and justify the differences