Question

The desired superannuation withdrawal amount for a person is $20,000, and the overall interest rate is 3%.

Desired annual income for ages 65 to 85, inclusive is $60,000. This annual amount is paid on each birthday, starting at age 65, and ending at 85. This stream of annual payments is what we refer to below as the user's retirement income stream.

Calculate the reduction in the user's retirement income stream by making the withdrawal from the user's superannuation fund.

Answer 1

Sol :

To determine reduction in the user's retirement income stream by making the withdrawal from the user's superannuation fund is the present value of withdrawal from superannuation fund as follows,

Withdrawal from superannuation (P) = 20000

Interest rate (r) = 3%

Number of withdrawals from age 65 to 85 inclusive of age 65th birthday (n) = 21

Present value of annuity = P x (1-(1/(1+r)^n))/r

Present value of annuity = 20000 x (1-(1/(1+3%)^21))/3%

Present value of annuity = 20000 x (1-(1/(1+0.03)^21))/0.03

Present value of annuity = 20000 x (1-(1/(1.03)^21))/0.03

Present value of annuity = 308300.48

Therefore the reduction in the user's retirement income stream will be $308300.48