8 You want to retire in 20 years and you would like to suppo

8. You want to retire in 20 years, and you would like to support an annual spending of $80,000. You plan to live 30 years in retirement. Your investment will ear 12% before retirement and 6% in retirement. () How much do you have to save each year? (i) What if you have 30 years to save before retirement? (iii) What if you only have 15 years? 9. You want to retire in 20 years, and you are able to save$8,000 per year before retirement. You plan to live 30 years in retirement. Your investment will ear 12% before retirement and 6% in retirement. (i) (i) (iii) How much will you have for spending each year in retirement? What if you have 30 years to save before retirement? What if you only have 15 years?

Solution

8) (i) The amount required at the end of 20 years to support an annual spending of $80000 (assumed to occur at the end of the year from year 21) = PV of the ordinary annuity of 80000 = 80000*(1.06^30-1)/(0.06*1.06^30) = $ 11,01,186.49 The above amount is the FV of the annual savings, which is again an ordinary annuity, but with an interest rate of 12%. The annual savings required = 1101186.49*0.12*1.12^20/(1.12^20-1) = $     1,47,425.50 (ii) The annual savings required = 1101186.49*0.12*1.12^30/(1.12^30-1) = $     1,36,705.32 (iii) The annual savings required = 1101186.49*0.12*1.12^15/(1.12^15-1) = $     1,61,680.87 9) (i) The amount that would be accumulated by the 20th year, is the FV of the ordinary annuity of 8000 for 20 years. The FV = 8000*(1.12^20-1)/(0.12) = $     5,76,419.54 The above FV is the PV of the annual amount available for spending for 30 years. The annual amount for spending = 576419.54*(0.06*1.06^30)/(1.06^30-1) = $        41,876.25 (ii) The FV = 8000*(1.12^30-1)/(0.12) = $ 19,30,661.47 The annual amount for spending = 1930661.47*(0.12*1.12^30)/(1.12^30-1) = $     2,39,679.38 (iii) The FV = 8000*(1.12^15-1)/(0.12) = $     2,98,237.72 The annual amount for spending = 298237.72*(0.06*1.06^30)/(1.06^30-1) = $        21,666.65