1. Chen plans to save 23,300 dollars per year for 6 years. His first savings contribution...

1. Chen plans to save 23,300 dollars per year for 6 years. His first savings contribution is expected later today. He then plans to make withdrawals for 6 years. How much can Chen expect to withdraw each year if he expects to earn 10.07 percent per year, he makes equal annual withdrawals, and his first withdrawal is made in 7 years?

Solutions

Expert Solution

Computation of future value of 6 annual savings:

FV of annuity due = (1+r) x P x [(1+r) ⁿ -1/r]

r = Rate of return = 0.1007 p.a.

P = Periodic deposit = $ 23,300

n = Number of periods = 6

FV = (1+0.1007) x $ 23,300 x [(1+0.1007)⁶ – 1/0.1007]

= 1.1007 x $ 23,300 x [(1.1007)⁶ – 1/0.1007]

= $ 25,646.31 x [(1.77833591227 – 1)/0.1007]

= $ 25,646.31 x (0.77833591227/0.1007)

= $ 25,646.31 x 7.7292543423

= $ 198,226.85

$ 198,226.85 is value of fund to facilitate 6 annual cash withdrawals which can be computed using formula for PV of annuity as:

PV = C x [1 – (1+r)^-n/r]

C = PV/ [1 – (1+r)^-n /r]

C = $ 198,226.85/ [1 - (1+0.1007)^-6 /0.1007]

= $ 198,226.85/ [1 - (1.1007)^-6 /0.1007]

= $ 198,226.85/ [(1 - 0.562323458184)/0.1007]

= $ 198,226.85/ (0.437676541816/0.1007)

= $ 198,226.85/4.346341031

= $ 45,607.75

Chen can withdraw $ 45,607.75 annually for 6 years.

jeff jeffy answered 1 year ago

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