Question

On the day you retire you have $1,000,000 saved. You expect to live another 25 years during which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually. Assume you want to spend the same amount each year in real terms and die on the day you spend your last dime. What real amount will you be able to spend each year?

Answer 1

Real Amount is the first annuity payment after retirement, as after first year amount will increase by 2.50%,

So,

Calculating Annuity Payment for Growing Annuity,

Payment = PV*[(r-g)/(1 - ((1+g)/(1+r))ⁿ)]

Payment = 1,000,000(0.0619 - 0.025)[(1 - (1.025/1.0619)²⁵)]

Payment = $62,867.72

So,

Real Payment = $62,867.72