You want to be able to withdraw $45,000 each year for 30 years. Your account earns...

You want to be able to withdraw $45,000 each year for 30 years. Your account earns 5% interest.

a) How much do you need in your account at the beginning?

$

b) How much total money will you pull out of the account?

$

c) How much of that money is interest?

Solutions

Expert Solution

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a) Correct Answer : 11778.46

Present Value of annuity is given by the formula,

PV = P [{ 1 - (1+r) -n } / r]

Where,

· Perodic Period

· Rate per period

· n = number of periods

Now substituting the values,

· Here P = $ 45,000

· r = 0.05

· n= 30

The present value of annuity = 45,000 [ { 1 - (1+0.05) -30 } / 0.05]

= 45,000[ { 1 - (1.05) -30 } / 0.05]

= 45,000[ (1 - 0.2314) / 0.05]

= 45,000 [ (0.7686) / 0.05]

= 45,000 X 15.3725

= $ 691760.296

Thus ,you need $ 691760.296 in your account at the beginning.

Part b)

Total money will you pull out of the account = Period withdrawals X Amount of withdrawals

Therefore, Total money will you pull out of the account = 30 X 45,000 = $ 1350000

Part c ) Money in the form of interest = Total money pull out - amount deposited in the beginning

Therefore, Total Interest = 1350000 - 691760.296 = $ 658239.704

jeff jeffy answered 1 year ago

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