Section 3B Putting Numbers in Perspective
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Transcript Section 3B Putting Numbers in Perspective
Section 4C
Savings Plans and Investments
Pages 246-268
Savings Plans and Investments
•The Savings Plan Formula
•Planning Ahead with Savings Plans
•Total and Annual Returns
•Types of Investments
Stocks
Bonds
Mutual Funds
Savings Plans
Deposit a lump sum of money and let
it grow through the power of
compounding (4B).
Deposit smaller amounts [in an
interest earning account] on a regular
basis (4A)
IRA’s, 401(k), Koegh, Pension
Special Tax Treatment
ex/pg246 You deposit $100 into a savings plan
at the end of each month. The plan has an APR
of 12% and pays interest monthly.
End of . . .
Prior
balance
Interest on
Prior Balance
End of
month
deposit
New
Balance
Month 1
0
0
100
$100
Month2
100
.01x100
=1
100
$201
Month 3
201
.01x201
=2.01
100
$303.01
Month4
303.01
.01x303.01
=3.03
100
$406.04
Month5
406.04
.01x406.04
=4.06
100
$510.10
Month6
510.10
.01x510.10
=5.10
100
$615.20
Is there a Savings Plan Formula?
APR n x Y
[(1
)
1]
n
A = PMT
APR
(
)
n
WOW !!!
where
A = accumulated savings plan balance
PMT = regular payment amount
APR = annual percentage rate (decimal)
n = number of payment periods per year
Y = number of years
This formula assumes the same payment and compounding periods.
Where did this formula come from?
Another way to figure accumulated value.
After 6 months:
End of month1 payment is now worth $100 x (1.01)5
End of month2 payment is now worth $100 x (1.01)4
End of month3 payment is now worth $100 x (1.01)3
End of month4 payment is now worth $100 x (1.01)2
End of month5 payment is now worth $100 x (1.01)1
End of month6 payment is now worth $100
After 6 months:
100x(1.01)5+100x(1.01)4+100x(1.01)3+100x(1.01)2+100x(1.01)1+100
= 100 x ((1.01)5 + (1.01)4 + (1.01)3 + (1.01)2 + (1.01) + 1)
Do you see a pattern?
After 10 months:
A = 100
x
((1.01)9 + (1.01)8 + (1.01)7 + … + (1.01)2 + (1.01) + 1)
After 55 months:
A = 100
x
((1.01)54 + (1.01)53+ (1.01)52 + … + (1.01)2 + (1.01) + 1)
After N months:
A = 100x [(1.01)N-1+(1.01)N-2+(1.01)N-3+ …+(1.01)2+(1.01)+1]
BN-1 + BN-2 + BN-3
N
B
1
+ … + B2 + B1 + 1 =
B-1
(1.01) N 1
A 100
1.01 1
(1.01) 1
100
.01
N
ex1/pg246-7 Use the savings plan formula to
calculate the balance after 6 months for an APR
of 12% and monthly payments of $100.
.12 12x ( 12 )
[(1
)
1]
12
A = 100
.12
( )
12
Calculator:
[(1 .01) 1]
A = 100
(.01)
6
0.06152
[(1.06152 1]
=
100
A = 100
.01
(.01)
= $615.20
= 100 6.152
ex2/pg248 At age 30, Michelle starts an IRA to save for
retirement. She deposits $100 at the end of each month. If she
can count on an APR of 8%, how much will she have when she
retires 35 years later at age 65? Compare the IRA’s value to her
total deposits over this time period.
.08 1235
[(1
)
1]
12
A = 100
.08
( )
Calculator:
12
[(1 .00667)420 1]
A = 100
(.00667)
[(1.00667)420 1]
= 100
(.00667)
ex2/pg248 At age 30, Michelle starts an IRA to save for
retirement. She deposits $100 at the end of each month. If she
can count on an APR of 8%, how much will she have when she
retires 35 years later at age 65? Compare the IRA’s value to her
total deposits over this time period.
[16.3152 1]
A = 100
(.00667)
[15.3152]
= 100
(.00667)
A = 100 2296.13
= $229613
ex2/pg248 At age 30, Michelle starts an IRA to save for
retirement. She deposits $100 at the end of each month. If she
can count on an APR of 8%, how much will she have when she
retires 35 years later at age 65? Compare the IRA’s value to her
total deposits over this time period.
The accumulated value of the IRA is $229,613
The value of the deposits is 35 x 12 x 100 = $42,000
[Compounding interest accounts for $229,613 - $42,000 = $187,613.]
WOW!
The Power of Compounding
ex3/pg250(Planning Ahead with Savings) You want to build a
$100,000 college fund in 18 years by making regular, end of the
month deposits. Assuming an APR of 7%, calculate how much
you should deposit monthly. How much of the final value comes
from actual deposits and how much from interest?
100000 = PMT
[(1
.07 1218
)
1]
12
.07
( )
12
[(1 .005833)216 1]
100000 = PMT
(.005833)
[(1.005833)216 1]
100000 = PMT
(.005833)
ex3/pg250(Planning Ahead with Savings) You want to build a
$100,000 college fund in 18 years by making regular, end of the
month deposits. Assuming an APR of 7%, calculate how much
you should deposit monthly. How much of the final value comes
from actual deposits and how much from interest?
[3.51229 1]
100000 = PMT
(.005833)
2.51229
100000 = PMT
.005833
100000 = PMT 430.70
100000/430.70 = PMT
$232.18 = PMT
ex3/pg250(Planning Ahead with Savings) You want to build a
$100,000 college fund in 18 years by making regular, end of the
month deposits. Assuming an APR of 7%, calculate how much
you should deposit monthly. How much of the final value comes
from actual deposits and how much from interest?
The monthly payments are $232.18.
The value of the deposits is 18 x 12 x 232.18 = $50,151
[The accumulated value of the fund is $100,000.]
[Compounding interest accounts for $100000 - $50151 = $49849.]
WOW!
The Power of Compounding
More Practice
47/246 Find the savings plan balance after 18 months with
an APR of 6% and monthly payments of $600
49/246 You set up an IRA with an APR of 5% at age 25. At
the end of each month you deposit $75 in the account. How
much will the IRA contain when you retire at age 65?
Compare the amount to the total amount of deposits made
over the time period.
53/246 You intend to create a college fund for your baby. If
you can get an APR of 7.5% and want the fund to have a
value of $75,000 after 18 years, how much should you
deposit monthly?
Homework
Pages 265-269
# 48, 50, 52, 54