Name_________________________________________________________
CCSS
A.SSE.1
Date __________
Compound Interest
The balance y of an account earning compound interest is given by
nt
r

y = P 1 +  ,
n

where P is the principal, r is the annual interest rate (in decimal form), n is the
number of times interest is compounded per year, and t is the time (in years).
The balance y of an account earning interest compounded continuously is given
by
y = Pe rt ,
where P is the principal, e is a mathematical constant (approximately 2.71828), r
is the annual interest rate (in decimal form), and t is the time (in years).
You and your friend have accounts earning compound interest. The account
balances are given below.
Your account:
y = 500(1.005)
12 t
Your friend’s account: y = 1000e0.12t
1. Describe how the interest is compounded in each account.
2. Which account has a greater annual interest rate? Explain your reasoning.
3. Which account has a greater principal? Explain your reasoning.
4. Do you think the balance of your account will ever exceed the balance of
your friend’s account? Explain your reasoning.
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Big Ideas Math
Performance Tasks
1
CCSS
A.SSE.1
A.SSE.1
Common Core State Standard
Interpret expressions that represent a quantity in terms of its
context.
a. Interpret parts of an expression, such as terms, factors, and
coefficients.
b. Interpret complicated expressions by viewing one or more of
their parts as a single entity.
CCSS
A.SSE.1
Grading Rubric
Answers
Score
1. Your account is compounded monthly. Your friend’s account is
4
compounded continuously.
2. your friend’s account; 12% > 6%
2
3. your friend’s account; $1000 > $500
2
4. no; Sample answer: Your friend’s account has a greater principal,
2
greater annual interest rate, and is compounded more frequently,
so it will increase at a greater rate.
Precision
1. Student interprets factors of the expressions to determine how
1
interest is compounded in each account.
2. Student interprets bases and exponents of the expressions to find
2
the annual interest rates and then compares them.
2
3. Student interprets and compares coefficients.
4. Student uses the comparisons of parts of the expressions to make a
conclusion about the balances.
Total Points
2
Big Ideas Math
Performance Tasks
1
16
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