Question

You estimate that by the time you retire in 35 years, you will have accumulated savings of $2 million. If the interest rate is 8% and you live 15 years after retirement, what annual level of expenditure will those savings support?

Answer 1

Answer:

We can use the present value of an annuity formula to determine the annual distribution. I'm assuming that your distributions will be made in a similar manner to an annuity due (the first payment happens when you retire).

annual distribution = principal balance / PV annuity factor

• principal balance = $2,000,000
• PV factor annuity due, 8%, 15 periods = 9.24424

annual distribution = $2,000,000 / 9.24424 = $216,350.94

if instead, the first distribution is received at the end of the first year of retirement, then the annual distribution will be:

annual distribution = principal balance / PV annuity factor

• principal balance = $2,000,000
• PV factor ordinary annuity, 8%, 15 periods = 8.55948

annual distribution = $2,000,000 / 8.55948 = $233,659.05