Good news: You will almost certainly be a millionaire by the time you retire in 50...

Good news: You will almost certainly be a millionaire by the time you retire in 50 years. Bad news: The inflation rate over your lifetime will average about 3.6%. a. 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.) b. What real annuity (in today’s dollars) will $1 million support if the real interest rate at retirement is 2.6% and the annuity must last for 20 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expert Solution

real value = nominal value / (1 + inflation rate)^{number of
years}

real value = $1,000,000 / (1 + 3.6%)⁵⁰

real value = $170,613.04

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. We need to calculate this.

r = interest rate per period. This is 2.6%.

n = number of periods. This is 20.

$170,613.04 = P * [1 - (1 + 2.6%)^-20] / 2.6%

P = $170,613.04 * 2.6% / [1 - (1 + 2.6%)^-20]

P = $11,047.99

Real annuity supported is $11,047.99

jeff jeffy answered 2 years ago

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