Suppose an individual makes an initial investment of $1900 in an account that ea

Question

Suppose an individual makes an initial investment of $1900 in an account that earns 7.5%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.) (a) How much is in the account after the last deposit is made? $ (b) How much was deposited? $ (c) What is the amount of each withdrawal? $ (d) What is the total amount withdrawn? $

Explanation / Answer

#(a)

we are "moving" a single payment plus an annuity up on the time graph for 144 periods

i = .075/12 = .00625

Amount at the end of 12 years

= 1900(1.00625)144 + 100(1.00625144 - 1)/.00625

= 27903.75

If we want the monthly withdrawals for the next 5 years, let that withdrawal be x

27903.75 = x( 1 - 1.00625^-60)/.0066667

27903.8 = 46.786 x

x = 27903.8 / 46.786

x = 596.413

# (b)

= 1900+100*144

=16300

#(c)

The present value of the annuity =

27903.75 = W*(1-(1+0.075/12)^(-60))/(0.075/12)

where W-the amount of each withdrawal

so, 27903.8 = 49.9053W

Hence, W = 27903.8/49.9053

W = 559.134

#(d)

= 559.134*60

= 33548.04

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