Annual payment = $5,000,000 / 20 = $250,000
PV = PMT + PMT
1
i
1
(1
i)
i
n

+
(for annuities due)
=
$250,000 + $250,000
1
.07
1
07(1.07)
.
19

= $250,000 + $250,000 [10.3356]
=$2,833,898.81.
5. (Q. 3 in B) Which of the following strategies will allow real retirement spending
to remain approximately equal, assuming savings of $1,000,000 invested at 8
percent annually, a 25year time horizon, and a 4 percent expected annual
inflation rate?
A) Spend approximately $63,000 annually.
B) Spend approximately $78,225 annually.
C) Spend approximately $93,680 annually.
D) Spend approximately $127,500 annually.
Answer A
Using the formula where 1 + real rate =
rate
inflation
1
rate
nominal
+
+
1
Real rate =
1.08
1.04.
– 1 = 3.85%.
Then using the formula where PV of an annuity =
+

×
t
)
r
1
(
r
1
r
1
C
$1,000,000 =
pmt
1
.0385
1
.0385(1.0385)
25

$63,001 =
pmt
.
6. (Q. 4 in B) You are saving money to buy a house in ten years.
You will need
$75,000 to make the down payment at that time.
Due to some other financial
commitments you won’t be able to deposit any money in years 9 and 10
towards
this down payment. How much equal amounts must you deposit in a savings
account at the end of each year (other than years 9 and 10) in order to save
$75,000 if the savings account pays interest at 10 percent per year compounded
annually?