MGCR 341: Finance 1
Summer 2010
Vadim di Pietro
Midterm: Version A: Solutions
1)
(5 points, 5 mins) Would you rather invest your money for one year at an APR of
6%
with monthly compounding, or at an APR of
6.1%
, where the compounding
frequency is such that the EAR is
6.3%
?
6% APR, with monthly compounding:
EAR = (1+6%/12)^12 – 1 = 6.17%
For the second option, you are told that the EAR is 6.3%, so you prefer the second option.
2)
(15 points, 25 mins) Today is year
t = 0
. You are planning for your retirement. Each
year in your retirement you would like to purchase the same amount of goods that
$50,000
can buy today. Assume that your first purchase will be made at
t = 31
and
your last purchase will be made at
t = 65
. The annual inflation rate is
3%
. The
risk free rate is
10%
.
a)
What is the Present Value of the cash flows you plan to spend in retirement? (You
may solve this question using either the nominal approach or the real approach.)
Nominal Approach:
This is a forward starting growing annuity with 65  31 + 1 = 35 cash flows. First required
nominal cash flow is $50,000 (1+0.03)^31 = $125,004.02 and the growth rate is 3%. Since the
first cash flow is at t = 31, you have to discount the result from the regular formula by 30
periods.
PV = [125,004.02/(0.1 – 0.03)] (1 – (1.03/1.1)^35) (1/(1.1^30)) = $92,092.81
Real Approach:
This is a forward starting constant annuity, where the real interest rate is 1.1/1.031 = 6.796%,
there are 35 cash flows and the first required real cash flow is $50,000. Since the first cash flow
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 Summer '09
 Jassim
 Zerocoupon bond, risk free asset

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