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Charlie wants to retire in 15 years, and he wants to have an annuity of $50,000...

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

Solutions

Expert 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

jeff jeffy answered 3 years ago
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