Complex Annuities
End of Period: Future Value
Saskatoon Ballpark Construction
Interest Rate: 5% per month
Proposed Expenditure Schedule:
$10,000,000 (end of Months 1 to 9)
$25,000,000 (end of Month 12)
$20,000,000 (end of Months 13 to 21)
$30,000,000 (end of Month 24)
It would be nice to have MLB games here!
Now we can finally add up the present
value of all expenditures. We have
With the net present value in hand, we can
send it the future. As a result, we have
How about equally distributed
expenditures?
Annuity
FV Factor
Why are the
numbers so high?
How could one
reduce costs?
21
12
13
21
1
1
1
1
(1
0.05)
(1
0.05)
PV
20,000,000
0.05
0.05
to
13
21
1
21
1
12
PV
PV
PV
to
to
to
13
21
PV
20,000,000 (12.8212
8.8633)
to
13
21
PV
$79,158,021.42
to
1
9
12
24
13
21
PV
PV
PV
PV
ballpark
to
and
to
PV
71,078,216.76
23,222,972.76
79,158,021.42
ballpark
PV
$173,459,210.94
ballpark
Future Value
(FV )
Present Value (PV)
(1
)
t
t
t
r
24
FV
PV
(1
)
ballpark
ballpark
r
24
FV
173,459,210.94 (1
0.05)
ballpark
FV
173,459,210.94 3.2251
ballpark
FV
$559,423,291.42
ballpark
(1
)
1
FV
PV
(1
) , and FV
t
t
r
r
C
r
24
(1
0.05)
1
FV
559,423,291.42
0.05
ballpark
C
559,423,291.42
$12,570,745.26
44.5020
C