SOLUTION: You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest. a) How much do you need in your account at the beginning? b) How much tota

Algebra ->  Finance -> SOLUTION: You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest. a) How much do you need in your account at the beginning? b) How much tota      Log On


   



Question 1203101: You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest.
a) How much do you need in your account at the beginning?


b) How much total money will you pull out of the account?



c) How much of that money is interest?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The given parameter are;
P%5Bo%5D= The principal or initial balance in the account at the beginning

d+= The amount to be withdrawn each year =d=30000
r = The interest rate per annum =+8%=>r=0.08
k+= The number of periods the interest is applied in a year = k=1
n = The number of years withdrawal is made =n=+25

a. The amount that should be in the account at the beginning is given by the payout annuity formula as follows;

P%5Bo%5D=%28d%281-%281%2Br%2Fk%29%5E%28-nk%29%29%29%2F%28r%2Fk%29

substitute given values and we get:

P%5Bo%5D=%2830000%281-%281%2B0.08%2F1%29%5E%28-25%2A1%29%29%29%2F%280.08%2F1%29
P%5Bo%5D=%2830000%281-%281.08%29%5E%28-25%29%29%29%2F%280.08%29
P%5Bo%5D=25619.462852612596%2F0.08
P%5Bo%5D=320243.3


The amount needed in the account at the beginning,
P%5Bo%5D+=320243.3

b. The amount of money pulled out,
+A+=+n%2Ad
Therefore,
A+=+25%2A30000=750000

c. The amount of money received as interest,
I+=+A+-+P%5Bo%5D
I+=+750000+-+320243.3+=+429756.7