You expect to retire in 25 years and live another 30 years i

You expect to retire in 25 years, and live another 30 years in retirement. If you want to be able to spend S100,000 each year in retirement. How much do you have to save each year before retirement? Your investment will earn 12% pa. before retirement and 8% pa. afterwards. 6.

Solution

Step-1:Calculation of accumulated saving at the beginning of retirement Accumulated saving at the beginning of retirement is the present value of annual spend in retirement life. Present Value of annual withdrawl = Annual withdrawl x Present value of annuity of 1 = $          1,00,000 x 11.25778 = $ 11,25,778.33 Working: Present value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.08)^-30)/0.08 i 8% =             11.25778 n 30 Step-2:Calculation of annual saving till retirement Annual Saving = Accumulated saving at retirement/Future value of annuty of 1 = $ 11,25,778.33 / 133.3339 = $          8,443.30 Working: Future Value of annuity of 1 = (((1+i)^n)-1)/i Where, = (((1+0.12)^25)-1)/0.12 i 12% =             133.3339 n 25 Thus, Saving each year would be $ 8,443.30