Question

In: Finance

You have just retired with savings of $1.5 million. if you expect to live for 30 years and to earn 8% a year on your savings, how much can you afford to spend each year?

Formula question

You have just retired with savings of $1.5 million. if you expect to live for 30 years and to earn 8% a year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of the year.

Expert Solution

Future Value of an Annuity Due (Beginning of the year payment)

Future Value = $1,500,000

Annual interest rate (r) = 8.00% per year

Number of years (n) = 30 Years

Annual Payment (P) = ?

Therefore, Future Value of an Annuity Due = (1 + r) x P x [{(1+ r)ⁿ - 1} / r ]

$1,500,000 = (1 + 0.08) x P x [{(1 + 0.08)³⁰ - 1} / 0.08]

$1,500,000 = 1.08 x P x [(10.06265689 – 1) / 0.08]

$1,500,000 = 1.08 x P x [9.06265689 / 0.08]

$1,500,000 = 1.08 x P x 113.2832111

$1,500,000 = P x 122.3458680

P = $1,500,000 / 122.3458680

P = $12,260.32 per year

Therefore, the amount to be spend in ach will be $12,260.32

jeff jeffy answered 2 years ago

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