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FV:
invest today for $ tomorrow (interest) – If you invest $9.52 for 14 periods @ 9%, at the end of the 14
th
period you will have 
$9.52*(1.09)^14 = $31.81; or 14 (N), 9 (i/y),1 (PV), 0 (PMT), CPT – FV = $31.81.
FVA:
series of equal pmts rec’d at end of each
period – If you put away $9.52 @
end of each next 14 periods @
9% you will have  $9.52 * [(1.09)^14 + (1.09)^13 + … + (1.09)^2 +
(1.09) + 1] = $247.70; or 14 (N), 9 (i/y), 0 (PV), 9.52 (PMT), CPT – FV = 247.70.
PV:
how much needed to invest today to have $
tomorrow – If you want to have $9.52 @ end of 14 periods, at 9% you must put away  $9.52 * [1/(1.09)^14] = $2.84; or 14 (N),
9(i/y), 0 (PMT), 9.52 (FV), CPT – PV = 2.84.
PVA:
in order to with draw $9.52 @
end of each of the next 14 periods @
9% I must
put away  $9.52 * [1/(1.09) + 1/(1.09)^2 + … + 1/(1.09)^14] = $74.12; or 14 (N), 9 (i/y), 9.52 (PMT), 0 (FV), CPT – PV = 74.12.
PVAD/FVAD:
annuity due is a series of equal pmts rec’d at the
start
of each period (where as an annuity is a series of equal
pmts rec’d at the
end
of each period).
PVAD =
(1 +
I) * PVA and
FVAD =
(1 + I) * FVA.
***CHANGE CALC SETTING TO
ANNUITY DUE: “2
nd
” “BGN” “2
nd
” “SET” 
to undo, repeat same steps.
Calc is in annuity due mode when small BGN is in
screen***
If I want to withdraw $9.52 at the start of each of the next 14 periods at 9% 
$9.52 * [1/(1.09) + 1/(1.09)^2 + … + 1/
(1.09)^14] * (1.09) = $80.80; or 14 (N), 9 (i/y), 9.52 (PMT), 0 (FV), CPT – PV = 80.80.
You put away $1000 for your grandson on the
day he is born, at 10%  How much will he have when he turns 21?
21 (N), 10 (i/y), 1000 (PV), 0 (PMT), CPT – FV = $7400.25.
After reflection, you think maybe putting away $150 each birthday might be better – How much would he have when he turns 21?
21 (N), 10 (i/y), 0 (PV), 150 (PMT), CPT – FV = $9600.37.
Suppose you put the $150 away at the start of each year?
“BGN Mode” –
21 (N), 10 (i/y), 0 (PV), 150 (PMT), CPT – FV = $10,560.41.
Your daughter will be a freshman a year from now, each year of school
will cost $20,000, payable at the start of each year – at 10%, how much must you invest today to cover her tuition, assuming she
finishes in 4 years?
4 (N), 10 (i/y), 20000 (PMT), 0 (FV), CPT – PV = $63,397.31.
If you don’t put the money away until she starts,
how much is needed?
“BGN Mode” – 4 (N), 10 (i/y), 20000 (PMT), 0 (FV), CPT – PV = $69,737.04.
Suppose that you had the
foresight to put away enough for your daughter’s education when she was born – assuming that she will enter college at age 17, how
much should you have put away at 10%?
From the last problem, you need $69,737.04 when she starts (age 17) – so you need the
PV of that amount 17 years earlier – (PV of PVAD) – 17 (N), 10 (i/y), 0 (PMT), 69737.04 (FV), CPT – PV = $13,797.10.
It is your
25
th
birthday, you would like to retire at age 60 on $30,000 /yr – you think that you will live until age 85 – how much must you put
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 Spring '09
 Upton

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