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ACCT101 Quiz 2
Section L04, 05, 06
Problem
Maximum mark
Score
1
27
2
9
3
42
4
18
5
12
Total
108
S
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Problem 1: Time value of money (27 Points)
On your 22th birthday, you make a wish that you will retire on your 65th birthday and live
happily ever after.
You want to accumulate enough by then to provide yourself with $600,000 a
year for 30 years (the first payment will be on your 65th birthday).
Assume that interest rate is
9%.
A. (6 points) How much must you accumulate by the time you retire?
Since the first payment will start on your 65th birthday, and continue for 30 years. As of your
64th birthday, the payment is an annuity at $600,000 per year, for 30 years, that starts in the next
year. Use the present value of annuity formula:
$600,000 כ
1
0.09
െ
1
0.09 כ ሺ1 0.09ሻ
ଷ
൨ ൌ $6,164,192
Therefore, as of the 65th birthday, the value of the annuity is: $6,164,192 * 1.09 = $6,718,970.
The $6,718,970 is the value of the saving as of your 65th birthday, your retirement date.
B. (9 points) How much must you save each year until retirement in order to finance your
retirement consumption?
Assume the savings are put aside on your birthday of each year, the
first one is on your 29th birthday, and the last one is on your 65th birthday.
To calculate the annual savings, first calculate the value of the savings as of your 28th birthday.
$6,718,970
ሺ1 0.09ሻ
ଷ
ൌ $277,027.1
Therefore, the present value of your annual savings as of your 28th birthday should equal
$277,027.1.
Your annual savings starts on your 29th birthday, and have in total 37 payments.
Therefore, using the present value of annuity formula:
ܵܽݒ݅݊݃ݏ כ
1
0.09
െ
1
0.09 כ ሺ1 0.09ሻ
ଷ
൨ ൌ $277,027.1
ܵܽݒ݅݊݃ݏ ൌ $26,004.63
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C. (12 points) If your wish had been to establish a charitable foundation on your 65th birthday,
the foundation will donate $300,000 per year forever, how much do you need to save every year?
For the savings' start date and end date, refer to B. The first donation of $300,000 will be on your
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This note was uploaded on 06/16/2011 for the course ACCT 101 taught by Professor Na during the Fall '10 term at HKUST.
 Fall '10
 na
 Accounting

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