3. Money is placed into a fund continuously for 20 years at the rate of $4000 per year for the first 10 years and $2000 per year for the second 10 years. The fund earns an effective rate of interest of 4%. At the end of 20 years, the accumulated amount in the fund is used to buy a perpetuity-due with annual payments of R, 2R, 3R,..., first payment made at the end of 20 years. Determine R if the force of interest for the perpetuity is d= 0.05. (7 marks) 3. Money is placed into a fund continuously for 20 years at the rate of $4000 per year for the first 10 years and $2000 per year for the second 10 years. The fund earns an effective rate of interest of 4%. At the end of 20 years, the accumulated amount in the fund is used to buy a perpetuity-due with annual payments of R, 2R, 3R,..., first payment made at the end of 20 years. Determine R if the force of interest for the perpetuity is d= 0.05. (7 marks)