Question

How much at end of each 6 month for 3 years at j2 = 10% would you have to save in order to receive $600 at the end of each 6 months for 4 years afterward? (Round your answer to 2 decimal places.

Answer 1

Let’s compute value of fund to facilitate expected cash withdrawals using formula for PV of annuity.

PV = P x [1-(1+r) ^-n]/r

PV = Value of accumulate fund, one period prior to the cash withdrawal

P = Periodic cash flow = $ 600

r = Rate of return = 0.01/2 = 0.05 semi-annually

n = Number of periods = 4 x 2 = 8 periods

PV = $ 600 x [1- (1+0.05) ^-8]/0.05

     = $ 600 x [1- (1.05) ^-8]/0.05

     = $ 600 x [(1- 0.676839362028687)/0.05]

     = $ 600 x (0.323160637971313/0.05)

     = $ 600 x 6.46321275942626

     = $ 3,877.92765565575 or $ 3,877.93

Semi-annual deposit to accumulate a fund of $ 3,877.93 can be computed using formula for FV of annuity as:

FV = P x [(1 + r) ⁿ – 1/r]

P = FV / [(1 + r) ⁿ – 1/r]

n = Number of periods = 3 x 2 = 6

P = $ 3,877.93 / [(1+ 0.05)⁶ – 1/r]

= $ 3,877.93 / [(1.05)⁶ -1/0.05]

  = $ 3,877.93 / [(1.340095640625-1)/0.05]

= $ 3,877.93 / (0.340095640625/0.05)

= $ 3,877.93 / 6.8019128125

= $ 570.123450108543 or $ 570.12

$ 570.12 need to save 3 years semi-annually to get the desired cash outflow for 4 years.