Respuesta :
Answer:
(a) $2865.72
(b) $2000.00
Step-by-step explanation:
You want to know the amount Carolyn can withdraw from a $400,000 account earning 6% compounded monthly if (a) it is to last 20 years, and (b) it is to last indefinitely.
(a) Annuity
The withdrawal amount from an ordinary annuity is given by the formula ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where P is the amount invested at annual rate r, and n monthly withdrawals are made.
For the given conditions, the amount Carolyn can withdraw is ...
A = 400000(0.06/12)/(1 -(1 +0.06/12)^-240) ≈ 2865.72
Carolyn can withdraw $2865.72 at the end of each month if she wants it to last 20 years.
(b) Interest
If Carolyn wants her fund to last indefinitely, she can only withdraw the interest earned each month:
I = Prt . . . . . . where P is invested at annual rate r for t years
One month is 1/12 year, so the interest earned is ...
I = 400000(0.06)(1/12) = 2000.00
Carolyn can withdraw $2000 at the end of each month if she wants her account to last indefinitely.
