The All-Mighty Bank wishes to lend 100,000,000 to a South American country and would like to earn \2% on its investment.

Repayment of the loan will be by two equal annual payments, the first due in one year. It is estimated that, in any given year, there is a 20% chance that no payment will be made. There is also a 40% chance that half the payment will be made, and a 40%) chance of payment in full. If no payment is made the first year, it is assumed that there will be no payment the second year. It is considered possible, however, that there might be partial payment the first year and full, partial or no payment the second year. How much will the bank ask the country to repay each year?