Question

If you win a lottery payout of $500,000 today, then for how many years do you need to invest this amount at 6% per year in order to withdraw $100,000 every year forever? Assume the 6% per year is a return that you can depend on forever.

Answer 1

The present value of a perpetual annuity is given by formula P = A/i

A = annuity value

i = interest rate

Here, A = 100000, i = 0.06

P = 100000/0.06 = 1666666.67

We need to find no. of years in which invested value of 500000 will increase to 1666666.67

We use formula F= P*(1+i)^t

here P = 500000, F = 1666666.67, i = 0.06, t=?

1666666.67 = 500000 *(1+0.06)^t

(1.06)^t = 1666666.67 / 500000 = 3.3333

Taking log both sides

t= log 3.3333 / log 1.06

t = 20.66 years