Question

You plan on saving $10,000 a year (as a regular annuity) for the next 30 years.  You will then make equal withdrawals for each of the next 25 years (also a regular annuity).  If the interest rate is 10% over the first 30 years but only 8% for the remaining 25 years, what will be the amount of each withdrawal?  

Answer 1

The amount is computed as shown below:

Future value of $ 10,000 for 30 years is computed as follows:

Future value = Annual amount x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 10,000 x [ [ (1 + 0.10)³⁰ - 1 ] / 0.10 ]

= $ 1,644,940.227

This will become the present value as shown below:

Present value = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ]

$ 1,644,940.227 = Annual amount x [ (1 - 1 / (1 + 0.08)²⁵ ) / 0.08 ]

$ 1,644,940.227 = Annual amount x 10.67477619

Annual amount = $ 1,644,940.227 / 10.67477619

Annual amount = $ 154,095.99 Approximately

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