The textbook is Fundamentals of Actuarial Mathematics,Third Edition, by S. David Promislow. Show all work (please include formulas used).

A loan contract involves advances of 10 000 initially, 20 000 one year later, and 30 000 one year after that. This is to repaid by 20 yearly instalments beginning at time 3. The payments reduce by 5% each year (so, for example, if the first payment was 1000, the second would be 950, the third would be 902.50). Interest rates are 6% for the first 5 years, 7% for the next 5 years, and 8% after that. Find all payments and the outstanding balances at the end of each year, until the loan is fully discharged. Balances should be calculated after the payment due at the particular time is made