Suppose an individual makes an initial investment of $1100 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.)

Question

Suppose an individual makes an initial investment of $1100 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?
$ 1

(b) How much was deposited?
$ 2

(c) What is the amount of each withdrawal?
$ 3

(d) What is the total amount withdrawn?
$ 4

Mgraph · Answer

(a)The accumulated value=

1100(1+0.075/12)^144+ 100*((1+0.075/12)^144-1)/(0.075/12)=$25942

(b)1100+100*144=15500

(c)The present value of the annuity=

25942=W*(1-(1+0.075/12)^(-60))/(0.075/12)

where W-the amount of each withdrawal
W=519.82

(d)519.82*60=31189.47

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