Question

You
want to be able to withdraw $30,000 each year for 20 years. Your
account earns 7% interest.

How much do you need in your account at the beginning?

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

How much money of that is interest?

Answer #1

Sol :

PMT = $30,000

Interest rate (r) = 7%

Period (n) = 20 years

a) To determine amount needed in account (PV) at the beginning as follows,

Present value (PV) = PMT x (1-(1/(1+r)^n)/r

PV = $30,000 x (1-(1/(1+7%)^20)/7%

PV = $30,000 x (1-(1/(1.07)^20)/0.07

**PV = $317,820.43**

b) Total money will you pull out of the account,

= Withdrawal per year x number of years

**= $30,000 x 20 = $600,000**

c) Interest amount will be = Total withdrawal - PV

**= $600,000 - $317,820.43 = $282,179.57**

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