© clark creative education · 2020-03-18 · used in real-world problems. 6.ee.2d perform...


Interest Investigation

Ideal Unit: Ratio, Proportion & Percent Time Range: 3-5 Days Supplies: Pencil & Paper

Topics of Focus:

- Percent Applications

- Simple Interest

- Compound Interest

Driving Question “Does interest affect a person's financial decisions?”

Culminating Experience A simulation as a financial advisor working with clients.

Common Core Alignment:

o

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems.

6.EE.2d Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.

7.EE.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Procedures: A.) In “Interesting Interest”, students will complete problems involving interest on loans or savings accounts. The problems in these situations are simple interest problems with the formula I = Prt.

B.) In “To Buy… Or Not to Buy”, students will complete simple interest application questions where they have to help a buyer decide whether they should buy something or not. Many of these problems will also reinforce basic operations.

C.) In “The Money Tree”, students will begin problems with the Compound Interest Formula. The final problem can be solved with the compound interest formula, but since it is compounded monthly and the question regards 1 month into the future, it can be solved with the simple interest formula.

D.) In “Financial Advisor”, students will wear the hat of a financial advisor and determine plans tailored to an individual’s needs. These problems can be done by hand or in a computer lab with Microsoft Excel.

* Aspects of the project can be completed independently. The entire project does not need to be completed to have a great learning experience, though it is suggested because it will best scaffold the skills and context.


Interesting Interest

Few things in our world can be considered more powerful than interest. While that may seem like a silly statement, interest builds financial power like nothing else. It can keep individuals and companies wealthy while at the same time it can keep people struggling to pay down their debts. Interest is a payment for the use of money. If you put money in the bank, you are given interest in exchange for them having it. If you take out a loan, you will be required to pay back the amount with interest. In this assignment, you will analyze situations involving savings accounts, loans or credit cards. Recall I = Prt where P is principal (starting amount), r is interest rate (as a decimal) and t is time (in years).

William Task: Estimate his interest income.

William has put $5,000 of savings into a bank that will collect a 1% annual interest rate. Suppose he does not deposit any additional money, how much interest will he earn in 6 months?

Recall (I = Prt and in this case t = 6/12)

Kaitlin Task: Understand

her credit card debt.

Suppose Kaitlin has a credit card debt of $4,000, which has an annual rate of interest of 18%. On the bill, the minimum payment for the month is $60. Suppose Kaitlin pays back only the minimum required payment, what is the new balance Kaitlin has at the end of the month?

Name ___________________________ Date ________________


Arthur Task: Determine

his interest charge

Arthur has a credit card with a rate of 21%. His balance on June 20th starts at $650. Over the next 10 days, he spends $35 on gasoline, $130 on groceries, he received a credit of $28 for a refunded item and he spent $410 on a car repair. What is the final balance of his account and what would be the interest charge if he does not pay it by the end of the month?

Event Cost Balance

650

Thandie

Task: Determine the interest earned

on her savings account.

Thandie is beginning a savings account for her daughter. To start that account she put in $1,000 and plans to put in $100 each month. If the savings account has an annual interest rate of 1.25% and is compounded every month (interest added to the principal), how much money will be in the account after the sixth month?

Month Beginning Amount

Interest Rate Monthly Interest

End-of-Month Amount

1 $1,000 .00104 1.04 1001.04 2 1101.04

Samuel Task: Determine

the long-term growth of his certificate of

deposit.

Samuel has put $8,000 into a Certificate of Deposit (CD) with an interest rate of 3%. A CD is an account that has a higher interest rate, but the account holder is not allowed to withdraw the money for a certain amount of time. If Samuel’s CD lasts for five years, how much is it expected to be worth at the end?

Year Beginning Amount

Annual Interest Rate

Annual Interest

End-of-Year Amount

1 8000 .03 240 8240 2 8240


To Buy… or Not to Buy?

Making good financial decisions is sometimes more challenging than comparing prices. Perhaps the $80 coffee maker seems unnecessary, but if you consider that you spend $3 a day on Starbucks, then this machine will quickly pay for itself. When things get more expensive and loans are required, then these decisions become a lot more important. In this assignment, the individuals are on the verge of making a large purchase, which will require a loan. They are all asking themselves, “Should I buy?”

Help these six people make decisions on these important purchases.

Mary Task: Must decide if a washer and dryer

is worth it.

Mary goes to the laundromat every week and it costs $5. She has found a combination washer/dryer that she could purchase for $1,200, but she would need to take out a loan. The local bank is offering her an 8% loan for the full amount. Would it be cheaper to borrow money on loan or continue going to the laundromat for the next five years? Assume the washer and dryer will be financed for the five years using simple interest. Which would cost more after 5 years: the loan or paying for weekly laundry? Should she buy it?

Arnold Task: Must decide

if he will buy a new car.

Arnold has paid off his car, but it is beginning to run into problems. He will consider buying a new car if the monthly payment is less than $200. He is looking at a $14,000 car with an interest rate of 5% simple interest for 3 years. Should he buy it?

Hint: An estimated monthly payment can be found with the formula 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 + 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑀𝑜𝑛𝑡ℎ𝑠

Name ___________________________ Date ________________


Andy Task: Must decide whether or not to buy a home gym.

Andy has a membership at a gym, but has considered purchasing a home gym so that he can exercise whenever he wants. His membership costs him $80 a month and the home gym costs $2,200. He would get a loan for the gym at an interest rate of 6%. Would it be cheaper to borrow money on loan or continue going to the gym for the next three years? Assume the home gym will be financed for the three years using simple interest. Which would cost more after 3 years: the loan or paying for the gym membership? Should he buy it?

Sydney

Task: Must choose a bank.

Sydney is purchasing new windows for her home, which have been quoted for $18,000. She would take out a loan with a 7.5% interest rate for five years. She is expecting that the windows will add $25,000 of value to her house for resale. Will she spend more than that overall or should she buy it?

Lou


Lou buys bottles of water from the grocery store, but is now considering the environmental ramifications of the waste. He is considering getting a water filtration system in his home, but it will cost $1,000, which would mean he would take out a small loan at 7% interest for one year. If bottled water costs $7 a week, what would be the difference in the costs after one year?

Safiyo Task: Must choose

a bank.

Safiyo is considering remodeling her hotel, which will cost her $460,000. The loan would be for 12 months at an interest rate of 4%. After the remodel, she will have 10 more suites available for guests, which will cost $130 a night. She will do it if she can earn the money back in a year. If you assume the rooms are booked every night of the year, does Safiyo earn her money back?


Ihe Money Tree

Despite popular belief, for some, money seems to grow on trees. Famous billionaire Warren Buffet has been quoted as saying his wealth has come from “a combination of living in America, some lucky genes, and compound interest.” While it’s not likely that the average person will turn their savings into billions, carefully making financial choices involving interest is key to personal financial stability. In this assignment, individuals are in a position where they have to make a choice. What is the best bank account? Which certificate of deposit will earn the most income? Which is the best credit card offer? Is it worth it to refinance our home? Analyze their situations and help them decide!

Help these six people make their personal finance decisions.

Tad


Tad’s bank is closing and he needs to make a choice on a new one. He has $15,000 in his savings account and has three offers for his new bank. He will choose the bank where his account will have the most value at the end of the year. Use the compound interest formula to decide which bank he should choose

𝐴 = 𝑃(1 +𝑟𝑛)

!"

Ameribank Huffington Sixth-Third

A savings account with 1.05% interest

compounded annually.


compounded monthly.


compounded weekly.

Jessica Task: Must choose

a loan.

Jessica has $4,000 in her savings that she plans to invest in a Certificate of Deposit. She has the following options on the table. Help her decide which one to choose. Provide your reasoning. Use the compound interest formula to decide which bank he should choose.

𝐴 = 𝑃(1 +𝑟𝑛)

!"

Capital Two J.C. Porgan Silverman Slacks

A 3.75% interest rate compounded monthly

for 4 years.


for 2 years.


for 3 years.

Name ___________________________ Date ________________


Enrique


Enrique is a recent college graduate and he has two different credit card offers. He is supposing he has a debt of $1,000 on the card. What would be the difference in the finance charges of these two credit cards for the next three months? The interest on a credit card always compounds at the end of the month.

Use the compound interest formula to decide which bank he should choose.

𝐴 = 𝑃(1 +𝑟𝑛)

!"

American Expression VISTA

A 15% interest rate with an annual fee.

An 18% interest rate with no annual fee.

If the annual fee of the American Expression card is $20, does this affect your choice? Why or why not?

Ting Fen Task: Must choose

a bank.

Ting Fen is considering jumbo Certificates of Deposit for her business. She has $200,000 to invest and is researching the difference in these two options. Use the compound interest formula to decide which bank he should choose.

Chevy Stanley Morgan

A 2.75% interest rate compounded quarterly for 2 years.

A 2.65% interest rate compounded monthly for 2 years.

Donnie Task: Must decide

to refinance his house.

Donnie currently pays about $400 in interest every month on his mortgage. He owes $100,000 on the mortgage and has been offered a 2.85% interest rate, which compounds monthly. What would be the monthly interest payment with the new offer and what is the monthly savings? It will cost $5,000 to refinance. How many months would it take to save $5,000? Is it worth it?


Financial Advisor

Cranking out formulas and punching calculators is the easy part, but can you put this research into action? In this project, you will work as a Financial Advisor for a few recent college graduates. They have just started their post-college careers and need to make important spending and saving decisions. It is your job to help them navigate the demanding world of personal finance.

Goal: To get out of debt and pay down his loan faster. After a dental emergency, DeAndre had to use his credit card to pay for the repairs. He currently has a debt of $800 remaining (which has an interest rate of 15%). He is currently paying his minimum monthly payment, which is $50. If he can increase his payment to $75, how many months earlier will he pay off his debt? How much money will he save on interest?


after payment

Interest Rate

Monthly Interest

End-of-Month

Amount

1 $800 0.0125


after payment

Interest Rate

Monthly Interest

End-of-Month

Amount

1 $800 0.0125

DeAndre

Name ___________________________ Date ________________


Goal: To decide which loan is better for her. After her car broke down, Bella is in the market for a new used car. There is a certified used sedan for $6,000, but she is unsure about the loans. She is considering a 24-month loan, a 36-month loan, and a 48-month loan but needs to know what the monthly payments and long term costs would be.

An estimated monthly payment can be found with the formula

𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 + 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑀𝑜𝑛𝑡ℎ𝑠

where Interest will be equal to I = Prt (where t is in years). Bella can afford about $200, but doesn’t want to pay too much interest.


6.75% for 24 months 7.00% for 36 months 7.25% for 48 months

Total Interest

Total Interest

Total Interest

Overall Cost

Overall Cost

Overall Cost

Monthly Payment

Monthly Payment

Monthly Payment

Which loan should Bella choose and what are your reasons?

Bella


Goal: To save money for his young son. Dez has decided for his son’s sixth birthday that he will open a college savings account. He earned a $10,000 bonus from work and wants to put the entire amount into the savings account for the next 12 years. He has to choose between three different savings accounts. Which account will earn the most interest?

Use the compound interest formula to decide which bank he should choose

𝐴 = 𝑃(1 +𝑟𝑛)

!"


3.25% APR compounded monthly

3.15% APR compounded daily

3.3% APR compounded quarterly

Dez


Goal: To set up a retirement account. Tripiti’s parents have a hard time paying bills after retirement, so she is considering setting up a retirement account for herself so history won’t repeat itself! She is considering opening a Roth IRA and putting $3,000 every year, but she has learned she is allowed to deposit up to $5,500. She wants to compare the difference over 25 years. She has found that the expected annual interest rate of a Roth IRA is about 8%. How much money will she save in each case? How much more interest would she earn if she deposited $5,500?


after payment

Interest Rate

Annual Interest

End-of-Year

Amount

1 $3,000 0.08 2 3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25


after payment

Interest Rate

Annual Interest

End-of-Year

Amount

1 $5,500 0.08 2 3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

Which Roth IRA should Tripiti choose?

Tripiti

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Interesting Interest Few things in our world can be considered more powerful than interest. While that may seem like a silly statement, interest builds financial power like nothing else. It can keep individuals and companies wealthy while at the same time it can keep people struggling to pay down their debts. Interest is a payment for the use of money. If you put money in the bank, you are given interest in exchange for them having it. If you take out a loan, you will be required to pay back the amount with interest.

In this assignment, you will analyze situations involving savings accounts, loans or credit cards. Recall I = Prt where P is principal (starting amount), r is interest rate (as a decimal) and t is time (in years).

William Task: Estimate his interest income.

William has put $5,000 of savings into a bank that will collect a 1% annual interest rate. Suppose he does not deposit any additional money, how much interest will he earn in 6 months?

Recall (I = Prt and in this case t = 6/12) William will earn 25 dollars of interest.

Kaitlin Task: Understand

her credit card debt.

Suppose Kaitlin has a credit card debt of $4,000, which has an annual rate of interest of 18%. On the bill, the minimum payment for the month is $60. Suppose Kaitlin pays back only the minimum required payment, what is the new balance Kaitlin has at the end of the month? I = Prt = (4000)(.18)(1/12) = $60. Thus at the end of June, Kaitlin will owe P = 4000 + 60 – 60 = $4000! Kaitlin has made no progress in paying down her credit card debt.


Arthur Task: Determine his

interest charge

Arthur has a credit card with a rate of 21%. His balance on June 20th starts at $650. Over the next 10 days, he spends $35 on gasoline, $130 on groceries, he received a credit of $28 for a refunded item and he spent $410 on a car repair.

What is the final balance of his account and what would be the interest charge if he does not pay it by the end of the month?

Event Cost Balance

650

Gas +35 685

Groceries +130 815

Refund -28 787

Car +410 1197

$20.95 will be charged as interest.

Thandie Task: Determine the interest earned on

her savings account.

Thandie is beginning a savings account for her daughter. To start that account she put in $1,000 and plans to put in $100 each month. If the savings account has an annual interest rate of 1.25% and is compounded every month (interest added to the principal), how much money will be in the account after the sixth month?


Interest Rate Monthly Interest

End-of-Month Amount

1 $1,000 .00104 1.04 1001.04 2 1101.04 .00104 1.15 1102.19 3 1202.19 .00104 1.25 1203.44 4 1303.44 .00104 1.36 1304.80 5 1404.80 .00104 1.46 1406.26 6 1506.26 .00104 1.57 1507.83

$1507.83 will be in the savings account after 6 months.

Samuel Task: Determine the long-term growth of

his certificate of deposit.

Samuel has put $8,000 into a Certificate of Deposit (CD) with an interest rate of 3%. A CD is an account that has a higher interest rate, but the account holder is not allowed to withdraw the money for a certain amount of time. If Samuel’s CD lasts for five years, how much is it expected to be worth at the end?


Annual Interest Rate

Annual Interest

End-of-Year Amount

1 8000 .03 240 8240 2 8240 .03 247.20 8487.20 3 8487.20 .03 254.62 8741.82 4 8741.82 .03 262.25 9004.07 5 9004.07 .03 270.12 9274.19

Samuel’s CD will be worth $9274.19 by the end of the five years.


To Buy… or Not to Buy?

Making good financial decisions is sometimes more challenging than comparing prices. Perhaps the $80 coffee maker seems unnecessary, but if you consider that you spend $3 a day on Starbucks, then this machine will quickly pay for itself. When things get more expensive and loans are required, then these decisions become a lot more important. In this assignment, the individuals are on the verge of making a large purchase, which will require a loan. They are all asking themselves, “Should I buy?”

Help these six people make decisions on these important purchases.

Mary Task: Must decide if a washer and dryer

is worth it.

Mary goes to the laundromat every week and it costs $5. She has found a combination washer/dryer that she could purchase for $1,200, but she would need to take out a loan. The local bank is offering her an 8% loan for the full amount. Would it be cheaper to borrow money on loan or continue going to the laundromat for the next five years? Assume the washer and dryer will be financed for the five years using simple interest. Which would cost more after 5 years: the loan or paying for weekly laundry? Should she buy it? 5*52*5 = $1300 worth of Laundromat. 1200*.08*5 = $480 in interest for a total of $1680. The washer and dryer would cost more. She should not buy it.

Arnold Task: Must decide if he will buy a new

car.

Arnold has paid off his car, but it is beginning to run into problems. He will consider buying a new car if the monthly payment is less than $200. He is looking at a $14,000 car with an interest rate of 5% simple interest for 3 years. Should he buy it?

Hint: An estimated monthly payment can be found with the formula 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 + 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡


14000*.05*3 = $2100 in interest. 16,100 total cost / 36 months = $447.22 is the monthly payment. He should not buy this car. He should look for something much cheaper.


Andy Task: Must decide whether or not to buy a home gym.

Andy has a membership at a gym, but has considered purchasing a home gym so that he can exercise whenever he wants. His membership costs him $80 a month and the home gym costs $2,200. He would get a loan for the gym at an interest rate of 6%. Would it be cheaper to borrow money on loan or continue going to the gym for the next three years? Assume the home gym will be financed for the three years using simple interest. Which would cost more after 3 years: the loan or paying for the gym membership? Should he buy it? The interest of the home gym would be $396 (2200*.06*3) for a total of $2,596. The cost of the gym would be $2880. He should buy the home gym.

Sydney


Sydney is purchasing new windows for her home, which have been quoted for $18,000. She would take out a loan with a 7.5% interest rate for five years. She is expecting that the windows will add $25,000 of value to her house for resale. Will she spend more than that overall or should she buy it? The interest over 5 years would be $6750, so added to the $18,000 this would be less than $25,000. She should get her money back if she is confident it will add that much value to the home.

Lou


Lou buys bottles of water from the grocery store, but is now considering the environmental ramifications of the waste. He is considering getting a water filtration system in his home, but it will cost $1,000 which would mean he would take out a small loan at 7% interest for one year. If bottled water costs $7 a week, what would be the difference in the costs after one year? $1070 for the filtration system including interest. $364 for the bottles, so the difference would be $706.

Safiyo Task: Must choose a

bank.

Safiyo is considering remodeling her hotel which will cost her $460,000. The loan would be for 12 months at an interest rate of 4%. After the remodel, she will have 10 more suites available for guests which will cost $130 a night. She will do it if she can earn the money back in a year. If you assume the rooms are booked every night of the year, does Safiyo earn her money back? The interest will be $18,400 for a total cost of $478,400. The remodel will produce 10*130*365 = $474,500 worth of revenue. So she does not quite earn all of her investment back (she is short $3900).


Ihe Money Tree Despite popular belief, for some, money seems to grow on trees. Famous billionaire Warren Buffet has been quoted as saying his wealth has come from “a combination of living in America, some lucky genes, and compound interest.” While it’s not likely that the average person will turn their savings into billions, carefully making financial choices involving interest is key to personal financial stability.

In this assignment, individuals are in a position where they have to make a choice. What is the best bank account? Which certificate of deposit will

earn the most income? Which is the best credit card offer? Is it worth it to refinance our home? Analyze their situations and help them decide!

Help these six people make their personal finance decisions.

Tad Task: Must choose a

bank.

Tad’s bank is closing and he needs to make a choice on a new one. He has $15,000 in his savings account and has three offers for his new bank. He will choose the bank where his account will have the most value at the end of the year.


𝐴 = 𝑃(1 +𝑟𝑛)!"

Ameribank Huffington Sixth-Third A savings account with

1.05% interest compounded annually.

$157.50 in interest


compounded monthly.

$143.12 in interest


compounded weekly.

$150.74 in interest Americabank has the most interest earned by the end of the year, so that is what he should choose.

Jessica Task: Must choose a

loan.

Jessica has $4,000 in her savings that she plans to invest in a Certificate of Deposit. She has the following options on the table. Help her decide which one to choose. Provide your reasoning.


𝐴 = 𝑃(1 +𝑟𝑛)!"


A 3.75% interest rate compounded monthly for

4 years.

It will be worth $4646.25 after 4 years.


2 years.



3 years.


Is it worth $150 to keep it in the bank for another year? She could find other options with the money.


Enrique Task: Must choose a

bank.

Enrique is a recent college graduate and he has two different credit card offers. He is supposing he has a debt of $1,000 on the card. What would be the difference in the finance charges of these two credit cards for the next three months? The interest on a credit card always compounds at the end of the month.


𝐴 = 𝑃(1 +𝑟𝑛)!"

American Expression VISTA

A 15% interest rate with an annual fee.

$37.97 interest

An 18% interest rate with no annual fee.

$45.68 interest

If the annual fee of the American Expression card is $20, does this affect your choice? Why or why not? The VISTA is cheaper after you consider the annual fee, but in the long run, it may be worth it.

Ting Fen Task: Must choose a

bank.

Ting Fen is considering jumbo Certificates of Deposit for her business. She has $200,000 to invest and is researching the difference in these two options. Use the compound interest formula to decide which bank he should choose.

Chevy Stanley Morgan

A 2.75% interest rate compounded quarterly for 2 years.

The Interest earned is $11,268.36

A 2.65% interest rate compounded monthly for 2 years.

The Interest earned is 10,873.61

In this problem, Chevy earns more interest on her investment.

Donnie Task: Must decide to refinance his house

Donnie currently pays about $400 in interest every month on his mortgage. He owes $100,000 on the mortgage and has been offered a 2.85% interest rate which compounds monthly. What would be the monthly interest payment with the new offer and what is the monthly savings? (100,000)(.0285)(1/12) = 237.50. So the savings would be $162.50 per month. It will cost $5,000 to refinance. How many months would it take to save $5,000? Is it worth it? It would take nearly 31 months before the savings added up to the cost of the refinance. If he is moving in the next 3 years, it is not worth it. If he will be there long-term, it could be.


Financial Advisor

Cranking out formulas and punching calculators is the easy part, but can you put this research into action? In this project, you will work as a Financial Advisor for a few recent college graduates. They have just started their post-college careers and need to make important spending and saving decisions. It is your job to help them navigate the demanding world of personal finance.

DeAndre

Goal: To get out of debt and pay down his loan faster. After a dental emergency, DeAndre had to use his credit card to pay for the repairs. He currently has a debt of $800 remaining (which has an interest rate of 15%). He is currently paying his minimum monthly payment which is $50. If he can increase his payment to $75, how many months earlier will he pay off his debt? How much money will he save on interest? It will save $34 on interest and he will pay it off 6 months earlier.

Month

Beginning Amount

(after payment)

Interest Rate

Monthly Interest

End-of-Month

Amount

1 $800 0.0125 $10.00 $810.00 2 $760.00 0.0125 $9.50 $769.50

3 $719.50 0.0125 $8.99 $728.49 4 $678.49 0.0125 $8.48 $686.97 5 $636.97 0.0125 $7.96 $644.94

6 $594.94 0.0125 $7.44 $602.37 7 $552.37 0.0125 $6.90 $559.28 8 $509.28 0.0125 $6.37 $515.64

9 $465.64 0.0125 $5.82 $471.47 10 $421.47 0.0125 $5.27 $426.73 11 $376.73 0.0125 $4.71 $381.44

12 $331.44 0.0125 $4.14 $335.59 13 $285.59 0.0125 $3.57 $289.16 14 $239.16 0.0125 $2.99 $242.14

15 $192.14 0.0125 $2.40 $194.55 16 $144.55 0.0125 $1.81 $146.35 17 $96.35 0.0125 $1.20 $97.56

18 $47.56 0.0125 $0.59 $48.15 19 ($1.85) 0.0125 ($0.02) ($1.87)

Month

Beginning Amount

(after payment)

Interest Rate

Monthly Interest

End-of-Month

Amount

1 $800 0.0125 $10.00 $810.00 2 $735.00 0.0125 $9.19 $744.19

3 $669.19 0.0125 $8.36 $677.55 4 $602.55 0.0125 $7.53 $610.08 5 $535.08 0.0125 $6.69 $541.77

6 $466.77 0.0125 $5.83 $472.61 7 $397.61 0.0125 $4.97 $402.58 8 $327.58 0.0125 $4.09 $331.67

9 $256.67 0.0125 $3.21 $259.88 10 $184.88 0.0125 $2.31 $187.19 11 $112.19 0.0125 $1.40 $113.59

12 $38.59 0.0125 $0.48 $39.08 13 ($35.92) 0.0125 ($0.45) ($36.37)


Bella

Goal: To decide which loan is better for her. After her car broke down, Bella is in the market for a new used car. There is a certified used sedan for $6,000, but she is unsure about the loans. She is considering a 24 month loan, a 36 month loan, and a 48 month loan but needs to know what the monthly payments and long term costs would be.

An estimated monthly payment can be found with the formula 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 + 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡


where Interest will be equal to I = Prt (where t is in years). Bella can afford about $200, but doesn’t want to pay too much interest.


6.75% for 24 months 7.00% for 36 months 7.25% for 48 months

Total Interest

6000*.0675*2 = $810

Total Interest

6000*.07*3 = $1260

Total Interest

6000*.0725*4 =$1740

Overall Cost

For a total of $6810

Overall Cost


Overall Cost


Monthly Payment

$283.75

Monthly Payment

$201.67

Monthly Payment

$161.25

Which loan should Bella choose and what are your reasons? If she can spare the $1.67, the second option will save her almost $500 in interest and an extra year worth of paying.


Dez

Goal: To save money for his young son. Dez has decided for his son’s sixth birthday that he will open a college savings account. He earned a $10,000 bonus from work and wants to put the entire amount into the savings account for the next 12 years. He has to choose between three different savings accounts. Which account will earn the most interest?


𝐴 = 𝑃(1 +𝑟𝑛)!"


3.25% compounded monthly

3.15% compounded daily 3.3% compounded quarterly

It would be worth $14,762.02 It would be worth $14,593.39 It would be worth $14,834.57

The third account earns the most interest and would be the best option for him.


Tripiti

Goal: To set up a retirement account. Tripiti’s parents have a hard time paying bills after retirement, so she is considering setting up a retirement account for herself so history won’t repeat itself! She is considering opening a Roth IRA and putting $3,000 every year, but she has learned she is allowed to deposit up to $5,500. She wants to compare the difference over 25 years. She has found that the expected annual interest rate of a Roth IRA is about 8%. How much money will she save in each case? How much more interest would she earn if she deposited $5,500?

Year

Beginning Amount

(after payment)

Interest Rate

Annual Interest

End-of-Year

Amount

1 $3,000 0.08 $240.00 $3,240.00

2 $6,240.00 0.08 $499.20 $6,739.20

3 $9,739.20 0.08 $779.14 $10,518.34

4 $13,518.34 0.08 $1,081.47 $14,599.80

5 $17,599.80 0.08 $1,407.98 $19,007.79

6 $22,007.79 0.08 $1,760.62 $23,768.41

7 $26,768.41 0.08 $2,141.47 $28,909.88

8 $31,909.88 0.08 $2,552.79 $34,462.67

9 $37,462.67 0.08 $2,997.01 $40,459.69

10 $43,459.69 0.08 $3,476.77 $46,936.46

11 $49,936.46 0.08 $3,994.92 $53,931.38

12 $56,931.38 0.08 $4,554.51 $61,485.89

13 $64,485.89 0.08 $5,158.87 $69,644.76

14 $72,644.76 0.08 $5,811.58 $78,456.34

15 $81,456.34 0.08 $6,516.51 $87,972.85

16 $90,972.85 0.08 $7,277.83 $98,250.68

17 $101,250.68 0.08 $8,100.05 $109,350.73

18 $112,350.73 0.08 $8,988.06 $121,338.79

19 $124,338.79 0.08 $9,947.10 $134,285.89

20 $137,285.89 0.08 $10,982.87 $148,268.76

21 $151,268.76 0.08 $12,101.50 $163,370.27

22 $166,370.27 0.08 $13,309.62 $179,679.89

23 $182,679.89 0.08 $14,614.39 $197,294.28

24 $200,294.28 0.08 $16,023.54 $216,317.82

25 $219,317.82 0.08 $17,545.43 $236,863.25

Year

Beginning Amount

(after payment)

Interest Rate

Anual Interest

End-of-Year

Amount

1 $5,500 0.08 $440.00 $5,940.00

2 $11,440.00 0.08 $915.20 $12,355.20

3 $17,855.20 0.08 $1,428.42 $19,283.62

4 $24,783.62 0.08 $1,982.69 $26,766.31

5 $32,266.31 0.08 $2,581.30 $34,847.61

6 $40,347.61 0.08 $3,227.81 $43,575.42

7 $49,075.42 0.08 $3,926.03 $53,001.45

8 $58,501.45 0.08 $4,680.12 $63,181.57

9 $68,681.57 0.08 $5,494.53 $74,176.09

10 $79,676.09 0.08 $6,374.09 $86,050.18

11 $91,550.18 0.08 $7,324.01 $98,874.20

12 $104,374.20 0.08 $8,349.94 $112,724.13

13 $118,224.13 0.08 $9,457.93 $127,682.06

14 $133,182.06 0.08 $10,654.56 $143,836.63

15 $149,336.63 0.08 $11,946.93 $161,283.56

16 $166,783.56 0.08 $13,342.68 $180,126.24

17 $185,626.24 0.08 $14,850.10 $200,476.34

18 $205,976.34 0.08 $16,478.11 $222,454.45

19 $227,954.45 0.08 $18,236.36 $246,190.80

20 $251,690.80 0.08 $20,135.26 $271,826.07

21 $277,326.07 0.08 $22,186.09 $299,512.15

22 $305,012.15 0.08 $24,400.97 $329,413.13

23 $334,913.13 0.08 $26,793.05 $361,706.18

24 $367,206.18 0.08 $29,376.49 $396,582.67

25 $402,082.67 0.08 $32,166.61 $434,249.28

Which Roth IRA should Tripiti choose? Is adding the extra money worth it? Over the 25 years, Tripiti will pay $62,500 more dollars if she paid the $5500 instead of the $3000, but it will result in the account being worth $197,386.03 more.


Interest Investigation

Rubric

Standards Exemplary Proficient Developing

7.EE.B.3 solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form

7.EE.B.4

use variables to represent quantities in a real-world or mathematical problem

use variables to construct simple equations to solve problems by reasoning about the quantities

Math Processes Exemplary Proficient Developing

Skills & Mechanics

accurately performs calculations

demonstrates fluency with mathematical skills and processes

Applications

accurately interprets word problems and addresses them with appropriate math skills

can articulate the meaning of calculations in the context of the problems.

Use of Evidence &

Analysis

can determine what evidence is appropriate to answer a question

utilizes mathematical outcomes to support their conclusions

C

Comm

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© clark creative education · 2020-03-18 · used in real-world problems. 6.ee.2d perform...

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