A man plans to retire on his 65th birthday in precisely four years’ time. The government will pay him a pension from age 68 of $10000 per annum monthly in advance. The man would like to purchase an annuity so that his income, including the government pension, is $16000 per annum paid monthly in advance from age 65 until his 78th birthday. He is to purchase the annuity by a series of payments made over four years quarterly in advance starting immediately.
Calculate the quarterly payments the man has to make if the present value of these payments is equal to the present value of the annuity he wishes to purchase at a rate of interest of 5% per annum e?ective. Mortality should be ignored.