Checklist
Notes
Part I
The Savings Plan Formula
Part II
Relative Change value of an investment.
Types of investments.
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Assignment
Notes
Assignment:
1. p 243 Quick Quiz
2. (Part I) p 244 - 245 Excercises 23, 25, 27, 33, 35
3. (Part II) p 245 -246 Exercises 37, 40, 47, 55, 59, 63
Practice using your calculator!
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Key Words - Part I
Notes
Savings Plan Formula
Our examples will deal with the situation of depositing
small amounts on a regular basis. This is common
because unlike the previous section, we are not always
able to deposit large sums of money.
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The Savings Plan Formula
Notes
Goal: You plan to deposit a regular payment (PMT) over
several periods in a year. As an example, a monthly
savings plan may look like this:
Month
1
2
3
4
Balance
$0.00
$50.00
$100.50
$151.51
Interest
$0
1% × $50.00 = $0.50
1% × $100.50 = $1.01
1% × $151.51 = $1.52
Deposit
$50.00
$50.00
$50.00
$50.00
New Balance
$50.00
$100.50
$151.51
$203.03
In this example, APR = 12%, or 1% per month, PMT =
$50.00 each month. The savings plan formula calculates
the accumlated balance or future value.
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The Savings Plan Formula
Notes
h
1+
A = PMT ×
APR (nY )
n
APR
n
i
−1
(1)
A is the accumalated balance
PMT is the regular payment (deposit) amount
APR is the annual percentage rate (as a decimal)
n is the number of compounding periods per year
Y is the number of years
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The Savings Plan Formula
Notes
Use the savings plan formula to calculate the balance
after 8 months for an APR of 12% and monthly payments
of $50.00.
8 months is 0.75 years.
h
A = PMT ×
= $50.00 ×
= $50.00 ×
(Math 1030)
i
APR (nY )
−1
n
APR
n
h
(12×0.75)
1 + 0.12
12
0.12
12
(1.01)8 − 1
1+
0.01
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i
= $414.28
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The Savings Plan Formula
Notes
Let us use these numbers for a retirement plan, but we
plan on retiring in 35 years. Our APR = 12%, and we still
deposit $50 each month. How much will we have after 35
years? Compare this value to our total deposits over this
time period.
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The Savings Plan Formula
Notes
Let’s aim for a goal (future value) of $100,000 in 20
years. How much should we deposit monthly, assuming an
APR = 6%?
How much of the $100,000 comes from deposits, and how
much from interest?
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The Savings Plan Formula
Notes
You now want to retire 25 years from now. During
retirement, you want to draw $40,000 per year for income,
forever. How can it be done? Assume a steady APR of
5.5%.
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