Question

An investor will deposit D dollars into an account with annual percentage rate r.

The investor has decided to withdraw W dollars every third year. So, at the beginning of the 3rd, 6th, 9th year, and so on, the investor withdraws W dollars.

Find an equation that shows the value of the account after N years. (Assume N is a multiple of 3. This will affect indexing. This assumption will simplify your answer. )

Here, record the part of your expression that involves the term D.

Here, record the part of your expression that involves the term W.

The investor will use this account for 15 years. The annual rate is 5%. And the withdrawal amount is 90,000 dollars. Find the amount D needed to cover this period.

Answer 1

ANSWER :

The given information is

The equation can be formed as follows:

We know that from the simple interest formula that if P is the principal amount , r is the annual interest rate and t is the time period ( in years)

Amount A = P ( 1 + rt )

Therefore, assuming N is a multiple of 3, we have

F(N) = Value of account after N years

F(N) = D(1 + rN) - W*N/3

1. Expression that Involves D = D(1+rN)

2. Expression that Involves W = W*N/3

Now, solving for D given withdrawl amount = 90,000

N=15 and r= 0.05

We have, total amount after 15 years with 5% interest rate = total withdrawn amount

D(1+ 0.05*15) =90000

D=

=

D= 51,428.57