Question

Suppose our retirement account pays 9% apr compounded monthly; what size nest egg do we need in order to retire with 25 years that yields to $5,000 per month? Show all work

Answer 1

$595,808.11

Explanation:

We assume the retirement account is intended to pay out $5000 per month for 25 years. The amortization formula can be used to find the required amount. The monthly payment A based on principal P with interest at annual rate r for t years satisfies the relation ...

A = P(r/12)/(1 -(1 +r/12)^(-rt))

P = A(12/r)(1 -(1 +r/12)^(-rt))

P = 5000(12/0.09)(1 -(1 +.09/12)^-300)

P = $595,808.11

The required nest egg is $595,808.11.