Good news: You will almost certainly be a millionaire by the time you retire in

Question

Good news: You will almost certainly be a millionaire by the time you retire in 45 years. Bad news: The inflation rate over your lifetime will average about 2.1%.

What will be the real value of $1 million by the time you retire in terms of today’s dollars? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

What real annuity (in today’s dollars) will $1 million support if the real interest rate at retirement is 2.9% and the annuity must last for 15 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

What will be the real value of $1 million by the time you retire in terms of today’s dollars? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

Solution.

a) 1,000,000 x 1.021^(-45) = 392,501.76
b) from part a, what can the 251,388 generate at 2.2% annually for 20 years?

392,501.76 (0.029) / (1 - (1.029)^-15)

= 11382.55 / 0.3488

= 32,633.45 per year (in today's dollars)

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