Answer:
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
