Illustrative Math - Algebra 1 - Unit 5 -Lesson 17

A couple has $5,000 to invest and has to choose between three investment options.Option A: 2\frac{1}{4}% interest applied each quarterOption B: 3% interest applied every 4 monthsOption C: 4\frac{1}{2}% interest applied twice each yearIf they plan on no deposits and no withdrawals for 5 years, which option will give them the largest balance after 5 years? Use a mathematical model for each option to explain your choice.

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2

Elena says that 6% interest applied semi-annually is the same as 1% interest applied every month: she reasons they are the same because they are both a 12% nominal annual interest rate.Is Elena correct that these two situations both offer a 12% nominal annual interest rate?

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2

Elena says that 6% interest applied semi-annually is the same as 1% interest applied every month: she reasons they are the same because they are both a 12% nominal annual interest rate.Is Elena correct that the two situations pay the same amount of interest?

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2

At the end of each year, 10% interest is charged on a $500 loan. The interest applies to any unpaid balance on the loan, including previous interest.Select all the expressions that represent the loan balance after two years if no payments are made.

• {"blocks":[{"key":"0","text":"500+2*(0.1)*500","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":15,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"500*(1.1)*(1.1)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":15,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"500+(0.1)+(0.1)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":15,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"0","text":"500*(1.1)^{2}","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":13,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"4ro68","text":"(500+50)*(1.1)","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[{"offset":0,"length":14,"key":0}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}}}}

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2

Here is a graph of the function f given by f(x)=100*2^{x}.Suppose g is the function given by g(x)=50*(1.5)^{x}.Will the graph of g meet the graph of f for any positive value of x? Explain how you know.

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2

Suppose m and c each represent the position number of a letter in the alphabet, but m represents the letters in the original message, and c represents the letters in a secret code.The equation c=m+7 is used to encode a message.Write an equation that can be used to decode the secret code into the original message.

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2

Suppose m and c each represent the position number of a letter in the alphabet, but m represents the letters in the original message, and c represents the letters in a secret code.The equation c=m+7 is used to encode a message.What does this code say: "AOPZ PZ AYPJRF!"?

Tags

A.SSE.1.a

F.IF.2

F.BF.1.a

A.SSE.1.b

N.Q.2