Question

In 2006, Harold deposited $10,000 in an account paying 9% annual interest. Harold wants to make five equal annual withdrawals from the account starting with the first withdrawal in 2018. Further, Harold wants to have exactly $30,000 left in the account in 2025. How large can each of the annual withdrawals be?

Answer: $2,763.50. Please show work.

Answer 1

Step 1:- selet base year

step 2 bring all your values at base year ( value of 10,000 and values of 5 withdraws)

step 3 discount the value 30,000 of 2025 to base year and now equate everything

step 4 solve for unknown

solving

base year selected is 2017

compunidng 10,000

value=10,000*(1.09)^11=25804.26405

suppose he withdraw x amount every five year.

value of all 5 withdraws = x(1/1.09 +1/1.09^2 + 1/1.09^3 +1/1.09^4 +1/1.09^5)

=x(3.88965).

Value of terminal = 30,000/ (1.09)^8 =15055.98839

now equate all three values

25804.26405 - x(3.88965) - 15055.98839 =0

x=2763.5

hence proved

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