Question

(a) By the end of this year you would be 35 years old and you want to plan for your retirement. You wish to retire at the age of 65 and you expect to live 20 years (I hope more) after retirement. Upon retirement you wish to have an annual sum of $50,000 to supplement your social security benefits. A conservative bond fund has been returning 7% annually and you decide to invest your retirement money in this fund. Assuming that the fund continues to return at least 7% during your planning horizon before and after retirement, how much should you invest in the fund starting from now, annually, in order to be able to withdraw $50,000 per year during your retirement?

Now let’s extend the problem so that you protect yourself against inflation.

(b) Suppose you think if you were to retire right now you would have needed $50,000 each year to supplement your social security and maintain your desired life style.

But because there is on average 3% annual inflation, when you retire in 30 years from now you need more than $50,000 per year to maintain the life style you like. (Hint: first calculate what future amount in 30 years is equivalent to $50,000 of now and then solve the rest of the problem).

Provide your explanations and definitions in detail and be precise. Comment on your findings. Provide references for content when necessary. Provide your work in detail

Answer 1

a)

The first step is to calculate the size of the withdrawl amount that would allow to withdraw $ 50,000 per year for 20 years. The size of the withdrawl is found using present value of annuity equation.

Size of the withdrawl = $ 529,700.71

Hence the retirement account must have $ 529,700.71 at the age of 65 years to withdraw $ 50,000 per year for 20 years.

The amount that must be invested now, annually  is found using the following equation

Solving for A in the above equation,

Annual investment = $ 5240.77

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b)

The future amount in 30 years that is equivalent to $50,000 now is found as follows

$50000 today is worth $ 121,363.1 in 30 years.

The next step is to find the size of the withdrawl considering that the inflation rate will continue to be 3% per year during the retirement years and also the returns from investing in the fund equals 7%.

Using the present value of growing annuity equation, we can find out the size of the retirement fund.

Size of the retirement fund = $ 1,617,971.99 $ 1,617,972 ( Taking inflation into account)

The amount that must be invested now, annually  is found using the following equation

The amount to be invested now, annually = $ 16007.95 $ 16008