1. pencil, red pen, highlighter, textbook, GP notebook, calculator
U3D1
Have out:
Bellwork:
Solve for x. (Hint: look for similarities on both sides of each equation.) 1) 2) 3) 4) +1 +1 +2 +2 +2 +2
total:

2. The account increased by 32%.
FX – 1
SIMPLE INTEREST
Suppose two credit unions offer to pay 8 percent annual interest. One advertises that it pays simple interest, and the other pays compound interest. We’ll investigate whether it makes any difference where you invest your money.
We will consider simple interest first. Suppose you deposit $100 in the first credit union and the interest on the $100 is paid at the end of each year. The “zero” year is your initial deposit.
year
Amount of money ($)
100.00 1
108.00 2
116.00 3
124.00 4
132.00
a) By what percent had your account increased at the end of the 4th year?
The account increased by 32%.

3. b) Continue this table for the next eight years.
FX – 1
b) Continue this table for the next eight years.
year
Amount of money ($)
100.00 1
108.00 2
116.00 3
124.00 4 5 6 7 8 9 10 11 12
c) Draw a graph to show the relationship between years and amount of money in the account. Is the graph arithmetic, geometric, or neither?
arithmetic 2 4 6 10 8 12
Years
Amount of $
100
120
140
160
180
200
132.00
140.00
148.00
156.00
164.00
172.00
180.00
188.00
196.00

4. FX – 2
COMPOUND INTEREST
The second credit union, like most financial institutions, pays compound interest. That means that interest is paid not only on the amount you invested (called the principal or initial value), but also on the accumulated interest. In other words, you earn interest on interest. To see this clearly, look at the table for compound interest. The interest rate is still 8% per year and the principal is still $
year
Amount of money ($)
100.00 1
108.00 2
116.64 3
125.97 4
a) Explain why the amount in your account at the end of the second year would be $
The interest is paid not only the amount invested, but also on the $8.00 accumulated interest earned during the 1st year.

5. The account increased by 36.05%. 136.05
FX – 2
COMPOUND INTEREST
b) Copy the table and enter the appropriate value for the 4th year. Be sure to round off appropriately (you can’t have fractions of a cent).
year
Amount of money ($)
100.00 1
108.00 2
116.64 3
125.97 4
c) The simple interest that the bank paid in 4 years increased your account 32%. According to the table where the interest was compounded, by what percent would your account increase for this same period?
The account increased by 36.05%.
136.05

6. Extend the table of compound interest for another 8 years.
FX – 3
Extend the table of compound interest for another 8 years.
year
Amount of money ($)
100.00 1
108.00 2
116.64 3
125.97 4 5 6 7 8 9 10 11 12
a) Draw a graph for the table of compound interest. Label each axis. Is the graph arithmetic, geometric, or neither?
geometric
100 2 4 6 10 8 12
Years
Amount of $
120
140
160
180
200
136.05
146.93
158.69
171.38
185.09
199.90
215.89
233.16
251.82

7. c) Which credit union would you use for your investment?
FX – 3
b) Should the graphs for the last 2 problems be discrete (points only) or continuous (connected)? Explain.
These are discrete graphs because the interest is earned once a year, not continuously throughout the year.
c) Which credit union would you use for your investment?
It is best to use the second credit that offers compound interest because the money grows faster.

8. Look back at the table you just made for compound interest.
FX – 4
Look back at the table you just made for compound interest.
a) Explain how to get the amount at the end of any year from the year above it.
Multiply by 1.08 to get the amount at the end of any year.
b) Represent the amount of money in your account after 2, 3, and 4 years using powers of 1.08.
t(2) = 100 (1.08)2
t(3) = 100 (1.08)3
t(4) = 100 (1.08)4
t(2) = $116.64
t(3)  $125.97
t(4)  $136.05
t(n) = 100 (1.08)n
c) Suppose you invested $1000 in this credit union for 20 years. How much money would be in your account at the end of 20 years.
t(20) = 1000 (1.08)20
t(20)  $

9. FX – 5
Suppose you have a younger sister and yesterday was her 6th birthday. She received $100 from your grandfather and you want to convince her to put it all in a savings account at the credit union. In order to convince your sister, you need to explain to her how much money she will have by her 18th birthday if the credit union is paying 8% annual interest compounded quarterly (4 times per year.)
a) If 8% is the annual interest, what is the quarterly interest? What is the quarterly multiplier? 8%
100% + 2%
= 102%
= 2% 4
multiplier = 1.02

10. multiplier = 1.02 t(10) = 100 (1.02)10 t(x) = 100 (1.02)x 18 – 6
FX – 5
multiplier = 1.02
b) Write an expression that represents the amount of money in the account after 10 quarters.
t(10) = 100 (1.02)10
c) Write an expression that represents the amount of money in the account after x quarters.
t(x) = 100 (1.02)x
d) Write an expression that represents the amount of money in the account on your sisters 18th birthday, and find the value of that expression.
The number of years that pass are:
18 – 6
= 12 years
Since there are 4 compoundings per year, then…
4 (12)
= 48 total compoundings
t(x) = 100 (1.02)x
t(48) = 100 (1.02)48
t(48)  $258.71

11. FX – 6
What if you could earn 12% per year compounded quarterly (3% per quarter) and you started with $356. Use the expression you wrote in the last problem as a model and write an equation for this new function where x still represents the number of quarters and y represents the amount of money you have at any time.
12%
= 3% 4
t(x) = 356 (1.03)x
100% + 3%
= 103% or
multiplier = 1.03
y = 356 (1.03)x
initial value = $356

12. Finish today's assignment:FX