Question

# You have just turned 40 years old and are trying to decide who much money to...

You have just turned 40 years old and are trying to decide who much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until you retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit. You decide that you will plan to live to 95 and work until your turn 65. You estimate that to live comfortably in retirement, you will need \$250,000 per year starting at the end of the first year of retirement and ending on your 95th birthday. You already have \$200,000 in the retirement plan. You will contribute the same amount to the plan at the end of every year that you work, starting next year. How much do you need to contribute each year to fund your retirement?

First, in this question, we need to calculate the amount that is needed to be accumulated at the 65th year, given the post retirement fund needs.

Per year required amount = \$250,000; n = 30 years, r = 7%

PV of an ordinary annuity is mathematically represented as:

PV (t = 65) = 250,000 * 12.4090

PV (t=65) = \$3,102,260.30 --> This is to be accumulated by the retirement through equal annual payments.

Let us first discount this amount to t=40 (today)

We will use basic TVM function for this purpose: PV = FV/(1 + r)n

PV = 3,102,260.30/(1 + 0.07)25

PV = \$571,588.91 --> PV of accumulated amount.

But you already have \$200,000 of this with you.

So, the amount to be accumulated in PV terms is \$571,588.91 - \$200,000 = \$371,588.91

Now, again using the PV of an annuity function to calculate the annual contribution requirement:

P= 31,866.2364 --> Amount to be accumulated yearly.

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