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Yeonjin9 Yeonjin9
wrote...
6 years ago
You have discovered a magical elixir that will allow you to live forever. You subsequently sold the rights to that elixir for $15,000,000 and have invested that money at 10% interest. The expected inflation rate is 2.5% forever. Finally, you wish to pay for your daughter’s wedding which you estimate will occur in 25 years. Measured in today’s dollars, you plan to spend $500,000 on the wedding. Assuming that you plan to never work again and that you wish to have the same purchasing power each year (excluding the wedding cost) during your retirement, what is the maximum amount you can withdraw during your first year of retirement? For simplicity, assume that the first withdrawal will occur in one year, the second in two years, etc
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wrote...
Staff Member
6 years ago
We expect to spend $500,000×1.02525 = $926,972 on the wedding.
Using the concept of indifference, we know that spending $926,972 in 25 years is equivalent to spending $926,972/1.125 = $85,556 today.

Said differently, if we set aside $85,556 today, it will have grown to $926,972 in 25 years. So, we effectively have $15,000,000-$85,556 = $14,914,444 available today for our retirement planning.

We know that the present value of a growing perpetuity is V0 = C1/(R-g), which gives us C1 = V0×(R-g). It follows that we can withdraw $14,914,444×(0.1-0.025) = $1,118,583 during our first year of retirement.
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