Suppose our retirement account pays 9% apr compounded monthly; what size nest egg do we need in order to retire with 25 years th

Question

jeyben [28]

3 years ago

7

Suppose our retirement account pays 9% apr compounded monthly; what size nest egg do we need in order to retire with 25 years th

at yields to $5,000 per month? Show all work

Mathematics

1 answer:

Natalka [10] · Answer 1 · 2022-02-13T20:26:50+03:00

Answer:

$595,808.11

Step-by-step 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.