An annuity on (50) provides for yearly payments for 30 years. The amount of the income is 10 000 for the first 10 years, 8000 for the next 10 years and 5000 for the last 10 years. The net single premium for this annuity is 100 000. You are given that the interest rate is a constant 5% and that 10p50 = 0.9, 20p50 = 0.8, 30p50 = 0.7. Find the premium if the same income is to be paid monthly instead of annually, assuming payments are made (a) at the beginning of each month, (b) at the end of each month.