COMPOUND INTEREST FORMULA
WORKSHEET
Activity A1
(homework review)
(time 5 min)
Match the terms with the meanings:
1
2
3
4
5
6
7
Savings Account
to deposit
Interests
Interest Rate
Principal
a
b
c
d
e
f
g
8
Amount/ Future Value
h
to withdraw
to earn
original amount invested
to take away money from a savings account of a bank
deposit of money in a bank
total of initial money and earned interests
to put money in a savings account of a bank
to receive money
money a customer may earn on his savings
is normally expressed as a percentage of the Principal
for a period of one year
Activity A2
(time 10 min)
Read the Investment problem below.
You have € 10000 you wish to deposit into a Savings Account. The bank offers you two
alternatives: the first Savings Account gives 10% annually, applying the Simple Interest. The
second Savings Account gives 10% annually, applying the Compound Interest.
By using a scientific calculator, individually complete the following table to find how much
money you will have, after 10 years, with the two options.
The first few are done for you.
Years After Initial
Deposit
0
1
2
3
4
5
6
7
8
9
10
Amount in Simple Interest
Account
€10.000
10000+10000⋅0,1= € 11000
11000+10000⋅0,1= € 12000
12000+10000⋅0,1= € 13000
1
Amount in Compound Interest
Account
€10.000
10000+10000⋅0,1= € 11000
11000+11000⋅0,1= € 12100
12100+12100⋅0,1= € 13310
COMPOUND INTEREST FORMULA
Compare your results in your pairs
Activity A3
(time 15 min)
With reference to the table of Activity A2, individually read the following report and then fill
in the blanks choosing among the words below:
Interests, rate, principal, not, more, constant, account, annual, same
SIMPLE AND COMPOUND INTEREST
An account earns Simple Interest when only the ………………… (original amount invested)
earns interest.
Therefore, as shown in the first column of the table, if you invest € 10000 at a 10% Simple
Annual Interest …………… for 10 years, you will earn € 1000 in the first year, another € 1000
in the second year and so on, giving a total of € 20000 in the ………………… after 10 years. The
annual growth of the account is ………………… and equals € 1000.
An account earning Simple Interest earns the ………………… amount of interest each year.
The final amount in a Savings Account after years of simple interest can be computed by
using the following formula:
A=P+ P⋅r⋅t =P( 1+r⋅t )
Simple Interest Account :
where: P= initial investment (principal)
r= annual interest rate (a percentage expressed in decimal)
t= number of years
A=
amount after t years
However, most accounts earn Compound Interest.
An account earns Compound Interest not only on the Principal, but also on the ………………… .
As shown in the second column of the table, if you invest € 10000 at a 10% Compound
………………… Interest rate for 10 years, you will earn € 1000 in the first year, € 1100 in the
second year, € 1210 in the third year and so on, giving a total of € 25937,42 in the account
after 10 years.
The annual growth of the account is not constant.
An account earning compound interest does …………… earn the same amount of interest
each year.
The Compound Interest Savings Account will have € 5937,42 ……………, at the end of the
period.
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COMPOUND INTEREST FORMULA
Discuss your choices in your pairs
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COMPOUND INTEREST FORMULA
Activity A4
(time 20 min)
Individually plot the information about the Simple Interest Savings Account from the first
column of the table in Activity A2, by using the year (time) as your independent variable and
the Amount (euro) in the Simple Interest Account as your dependent variable. For example:
plot (0 ;10000) , (1;11000 ) , (2;12000 ) , etc.; adjust the scale appropriately.
In your pairs, compare the graph obtained and answer the questions:
1. What pattern do you see?
2. Starting from the formula A=P(1+r⋅t ) , try to guess the equation that models this
data: y=................................
3. Now graph the equation. Does it fit the data?
4. How is the growth of the account in the Simple Interest Account each year?
Do the same with the Compound Interest Account. For example: plot
(1;11000 ) , (2;12100 ) , (3 ;13310 ) etc.; adjust the scale appropriately.
(0 ;10000) ,
In your pairs, compare the two graphs obtained and answer the questions:
5. Does the Compound Interest data fall on the graph of the equation above?
6. Is the growth of the Savings Account in the Compound Interest Account constant each
year?
7. Why, in the second year, is the interest earned on the Compound Interest Account
greater than the interest earned on the Simple Interest Account?
Go to
http://www.moneychimp.com/features/simple_interest_calculator.htm
where you can see the graphs of the functions representing the Simple and Compound
Interest (the year is used as the independent variable and the Amount as the dependent
variable).
In your pairs, compare the two graphs and discuss the answers to the questions
8. In which Savings Account is the amount of money increasing more rapidly?
9. Which Savings Account will have more money at the end of 10 years, assuming you do
not make any additional deposits or withdrawals?
10. Among the functions studied, what is in the graph that is similar to that of the
Compound Interest? And what is its equation?
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COMPOUND INTEREST FORMULA
Activity A5
(time 10 min)
Individually watch the 5 min. video at: https://www.youtube.com/watch?v=hSIBoQlJ6AA
If necessary, you can watch it again.
Activity A6
(time 15 min)
Read the following report about the Formula to calculate the total Amount when the interest
is compounded
The amount A in an account after years of compound interest can be computed using the
nt
( )
A=P 1+
following formula:
where:
Compound Interest Account
r
n
P= initial investment (principal)
r=
n=
t=
A=
annual interest rate (a percentage expressed in decimal)
number of compoundings per year (initially consider n=1)
number of years
amount after t years
Check this formula for the compound interest data by doing the following:
a. For the Compound Interest Account to the problem of Activity A2
P=.........................................
r=. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. .. . .. ..
n=
1
b. Use the formula to write an equation that models the data of the problem for
Compound Interest. Note that t is the independent variable (years) and A
the dependent variable (amount):
A=...........................................
c. Plot this equation to make sure that it fits the data plotted in Activity A4.
Check your results with your partner.
Apply the formula above to solve the following problems:
Robert puts $400.00 into an account to use for school expenses. The account earns 2%
interest, compounded annually. How much will be in the account after 6 years?
Round your answer to the nearest cent. (annual compounding)
5
is
COMPOUND INTEREST FORMULA
Suppose Karen has $1000 that she invests in an account that pays 3.5% interest
compounded quarterly. How much money does Karen have at the end of 5 years?
(not annual compounding)
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COMPOUND INTEREST FORMULA
Activity A7
Homework
Financial Advice
You have been hired as a financial advisor. Your first job is to advise a young couple about
which type of no-risk savings account to put their money in. They currently have €10.000.
The following options are available:
a. Put the money in an account earning 8,75% annual simple interest.
b. Put the money in an account earning 8% annual compound interest.
Write a report to the couple describing the implications of each of these options on their
future finances. Include graphs and computations comparing the amount of money in each
account over time.
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