If Bruce needs to withdraw $100 per year over the next 3 years beginning immediately, how much must he deposit today if his account earns 10%?

He has to deposit $ 273.55 today to withdraw $ 100 per year over next three years beginning immediately.                                                      

Explanation:

The problem belong to Present value of Annuity due. Annuity due formula is used when the series of payments/receipts takes place at the beginning of each time period.

Mathematically, Present value of annuity due can be calculated as;

Present value of Annuity Due = Amount of equal Payment or Withdrawal/interest rate[1-1/(1+interest rate)^ no.of time periods] x (1+interest rate) (A)

From given data in the problem,

Interest Rate = 10 %

No. of Time Period = 3

Payments/Withdrawal = $ 100

Put these values in equation  (A), we get

Present value of Annuity Due = $100 / 10 % x[1-1/(1+10 %)^3] x (1+10 %)

or We can also write as

Present value of Annuity Due = $100 / 0.10 x [1-1/(1+0.10 )^3] x (1+0.10 )

Present value of Annuity Due = $ 1000 x [1-1/(1.331)] x (1.10)

Present value of Annuity Due = $ 1000 x [1-0.751315] x (1.10)

Present value of Annuity Due = $ 1000 x 0.248685 x 1.10

Present value of Annuity Due = $ 273. 55

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