Charlie wants to retire in 15 years and he wants to have an

Charlie wants to retire in 15 years, and he wants to have an annuity of $50,000 a year for
20 years after retirement. Charlie wants to receive the fist annuity payment the day he
retires. Using an interest rate of 8%, how much must Charlie invest today in order to have his
retirement annuity

Solution

Step-1:Calculation of present value of annuity Present Value of annuity = Annuity x Present Value of annuity of 1 = $                  50,000 x 10.6036 = $        5,30,179.96 Working: Present Value of annuity of 1 = ((1-(1+i)^-n)/i)*(1+i) Where, = ((1-(1+0.08)^-20)/0.08)*(1+0.08) i 8% =                    10.6036 n 20 Step-2:Calculation of present value of above amount Present Value of above amount = Above Amount x Present Value of 1 = $        5,30,179.96 x      0.3152 = $        1,67,134.83 Working: Present Value of 1 = (1+i)^-n Where, = (1+0.08)^-15 i 8% =                      0.3152 n 15 Thus, Required investment today is $        1,67,134.83