Question

1. What single deposit of size $X into a fund paying 4% compounded annually is required at t = 0 in order to make withdrawals of $810 each at t = 4,5,6, and 7 and a single withdrawal of $1020 at t = 10? $

2. Using a 4% annual compound interest rate, what investment today is needed in order to withdraw $4,000 annually

a). for 10 years? $

b). for 10 years if the first withdrawal does not occur for 3 years? $

please answer both thank you

Answer 1

1. Calculation of PV

PV is Present value of all future cash flows discounting at required arte of return.

PV =

= 692.3914 + 665.7609 + 640.1548 + 615.5334 + 689.0755

PV = 3302.92 approx

2.

a) $4000 withdrawal per annum for 10 years

PV = Annuity x cumulative discounting factor @ 4% for 10 years

= 4000 x 8.1108957

= 32443.58

b) Withdraw $4000 from year 4 and onwards.

PV =

= 3419.2167 + 3287.7084 + 3161.2581 + 3039.6712 + 2922.7608 + 2810.3469 + 2702.2567

= 21343.2190