Question

You want to have $2 million in real dollars in an account when you retire in 50 years. The nominal return on your investment is 9 percent and the inflation rate is 4 percent. What real amount must you deposit each year to achieve your goal?

Answer 1

The amount is computed as shown below:

real rate is computed as follows:

= [ (1 + nominal rate of return) / (1 + inflation rate) ] - 1

= [ (1 + 0.09) / (1 + 0.04) ] - 1

= 0.048076923

So, the amount will be as follows:

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

$ 2,000,000 = Annual deposit x [ [ (1 + 0.048076923)⁵⁰ - 1 ] 0.048076923 ]

$ 2,000,000 = Annual deposit x 196.8312556

Annual deposit = $ 2,000,000 / 196.8312556

Annual deposit = $ 10,160.99 Approximately

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