A 15-year loan is to be repaid by installments of $100 at the end of year 1, $200 at the end of year 2, and so on, increasing by $100 each year, up to $800 at the end of the eighth year. From then onwards, a level installment of $800 will be paid. The rate of interest charged is 5.2%. Calculate the loan amount. What is the interest and the principal reduction in the 5th payment? Solve analytically