Transcript Section 3B Putting Numbers in Perspective
Section 4B Savings Plans and Investments
Pages 227-250
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 ( 4A ).
Deposit smaller amounts [in an interest earning account] on a regular basis ( 4B ) IRA’s, 401(K), Koegh, Pension Special Tax Treatment
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 . . .
Month 1 Month2 Month 3 Month4 Month5 Month6 Prior balance 0 $100 $201 $303.01
$406.04
$510.10
Interest on Prior Balance 0 .01x100
= $1 .01x201
=$2.01
.01x303.01
=$3.03
.01x406.04
=$4.06
.01x510.10
=$5.10
End of month deposit $100 $100 $100 $100 $100 $100 New Balance
$100 $201 $303.01
$406.04
$510.10
$615.20
Is there a Savings Plan Formula?
A
PMT 1
APR n
n
1 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
Where did this formula come from?
After 6 months: 100 x (1.01) 5 +100 x (1.01) 4 +100 x (1.01) 3 +100 x (1.01) 2 +100 x (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)
Where did this formula come from?
After N months: A = $100 x [(1.01) N-1+ (1.01) N-2 + (1.01) N-3+ … + (1.01) 2+ (1.01) + 1]
So
B N
1
B N
2
B N
3
B
2
B
1 B N 1 B - 1
N
1 1.01
N
2 1.01
N
3 1.01
1 1.01
N 1.01 - 1 1
A
$100
(1.01)
N
1.01
1 1
$100
(1.01)
N
.01
1
Use the savings plan formula to calculate the balance after 6 months for an APR of 12% and monthly payments of $100.
A
PMT 1
APR n APR n
1 1+ .12
12 12 12 1 2 1
Calculator:
[(1 .01) 6 1] (.01) [(1.06152...
1] (.01) 0.06152...
.01
= $615.20
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.
A
PMT 1
APR n APR n
1
1
.08
12
1
Calculator:
[(1 .00666...) 420 1] (.00666...) [(1.0066...) 420 1] (.0066...)
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.
[16.2925499...
1] (.00666...) [15.2925499...] (.00666...)
= $229,388
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 $229,388 The value of the deposits is 35 x 12 x 100 = $42,000 [Compounding interest accounts for $229,388 - $42,000 = $ 187,388 .] WOW!
The Power of Compounding
(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?
A
PMT 1
APR n APR n
1 [(1 .07
12 ) ( ) 12 1] [(1 .005833...) 216 1] (.005833...) [(1.005833) 216 1] (.005833)
(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?
(.005833...)
2.512539...
.005833...
$100,000/430.70210266... = PMT $232.17 = PMT
(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 $232.17.
The value of the deposits is 18 x 12 x $232.18 = $50,148.72
[The accumulated value of the fund is $100,000 .] [Compounding interest accounts for $100,000 - $50,148.72 = $49,851.28
.] WOW!
The Power of Compounding
More Practice
Find the savings plan balance after 18 months with an APR of 6% and monthly payments of $200.
1+ .06
12 12 1 1+.005
18 .005
1 $200 [.09392894] (.005) 5 78 791 $3 ,
More Practice
You set up an IRA with an APR of 5% at age 25. At the end of each month you deposit $50 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.
A = $50 1+ .05
12 12 1 A = $50 1+.004166...
480 .004166...
1 A = $50 6.358417...
.004166...
A = $76,301.00
total deposits
$24, 000
More Practice
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 $150,000 after 18 years, how much should you deposit monthly? [(1 .075
12 ) 1] ( .075
12 ) [(1 .00625) 216 1] (.00625) [2.8412535...] (.00625)
More Practice
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 $150,000 after 18 years, how much should you deposit monthly? $150,000 454.60056...
= PMT $329.96 = PMT