We included HMH Into Math Grade 7 Answer Key PDF Module 2 Lesson 5 Simple Interest to make students experts in learning maths.
HMH Into Math Grade 7 Module 2 Lesson 5 Answer Key Simple Interest
I Can calculate simple interest and the total value of an account after any period of time. I understand and can apply the equation I = Prt.
Step It Out
1. Big Money Bank loans $12,000 to Carlotta. This initial amount borrowed is called the principal.
Carlotta has to repay the loan to the bank at a rate of 5.5% simple interest per year over 8 years. What is the total amount of interest she will have to pay on her loan?
Connect to Vocabulary
Simple interest is a fixed percent of the principal. It is calculated using the formula I = Prt, where P represents the principal, r the rate of interest, and t the time.
A. Find the amount of simple interest I that Carlotta must pay after one year.
Simple interest, I
Carlotta must pay $____ in interest after one year.
Answer:
Simple interest I = principle, P x Annual interest rate, r.
Principle P = $12000
Annual interest rate = 5.5%
Simple interest I = $12000 x 5.5%
I = $660
Carlotta must pay $660 in interest after one year.
B. Calculate the total interest Carlotta must pay over the 8 years of the loan.
Interest paid over 8 years
Over 8 years Carlotta will pay ____ in simple interest on her loan.
Answer:
Interest paid over 8 years = interest paid in one-year x number of years.
Interest paid in one year = $660
Number of years = 8
Interest paid over 8 years = $660 x 8 = $5280
Over 8 years Carlotta will pay $5280 in simple interest on her loan.
Turn and Talk Before she took out her loan, a different bank offered Carlotta a $12,000 loan at 5% interest to be paid back over 9 years. Would that loan cost Carlotta more interest than the loan she took, or less? How much is the difference?
Answer:
Given that,
Principal = $12000
Interest rate = 5%
Number of years = 9
Simple interest = PTR
= $12000 x 5% x 9
= $5400.
Over 8 years Carlotta will pay $5280 in simple interest on her loan.
Over 9 years Carlotta will pay $5400 in simple interest on her loan.
The simple interest of the loan for 8 years is less than the 9 years of a loan.
The difference of the two loans is $5400 – $5280 = $120
2. Emilio opens a savings account at his local credit union with a $5,000 deposit. The account will pay 2.5% simple interest per year. How does Emilio’s account grow over time?
A. Find the amount Emilio’s account earns in interest each year.
Simple interest for 1 year
= P ∙ r
= ____ ∙ 0.025 = _____
Emilio’s account earns ____ per year in interest.
Answer:
Simple interest per 1 year = P x r
P = principle = $5000
R = interest rate = 2.5% = 0.025
Simple interest per 1 year = $5000 x 0.025
= $125
Emilio’s account earns $125 per year in interest.
B. Write an equation for the amount of interest l Emilio’s account earns in t years.
I = P. r ∙ ___
I = ___ t
Answer:
P = principle = $5,000
R = interest rate = 2.5% = 0.025
Time = t
I = P x r x t
I = $125t
C. How much interest will be added to Emilio’s account after 12 years? Show your calculation.
I = ___t
I = ____ ∙ ____ = ____
Answer:
I = $125t
T = 12 years.
Substitute t in the above equation.
I = $125(12)
= $1500
Interest added to Emilio’s account after 12 years is $1500
3. Melanie deposits $8,200.00 in a bank account paying 4.4% simple interest. How much money will be in her account after 5 years and 6 months?
A. Find the amount Melanie’s account earns in interest in 5.5 years.
I = P ∙ r ∙ t
I = 8,200 ∙ ____ ∙ ____
I = ____
The amount of interest in 5.5 years is $_____
Answer:
Given that,
Principal = P = $8200
Interest rate = 4.4%
Time = 5.5 years = 5 years and 6 months.
I = P x r x t
I = $8200 x 4.4% x 5.5
= $1984.4
The amount of interest in 5.5 years is $1984.4.
B. Find the total amount in Melanie’s account after 5.5 years.
Total amount
= P + I
= ___ + ___ = ____
Melanie’s account will contain $____ after 5 years and 6 months.
Answer:
Total amount = P + I
Principal = P = $8200
Simple interest I = $1984.4
Total amount = $8200 + $1984.4 = $10,184.4.
4. Gregory borrowed money as shown to buy a used car. It cost him $10,650 to repay the loan. How many years did Gregory spend repaying his loan?
A. Find the amount of simple interest I Gregory paid.
Total repaid = P + I
___ = 7,500 + ___
Gregory paid a total of ____ in interest.
Answer:
Simple interest I = PTR
Principal P = 7500
Interest rate = 6%
Time = 1 year
Simple interest I = $7500 x 6% x 1
= 450
Total Paid = P + I
Principal P = 7500
Simple interest I = $7500 + $450
= $7950
Gregory paid a total of $7950 in interest.
B. Find the time t in years that it took Gregory to pay off his loan.
I = P ∙ r ∙ t
3,150 = ___ ∙ ___ ∙ t
3,150 = ___ ∙ t
____ = t
Gregory spent ___ years paying back his loan.
Answer:
I = p x r x t
Principal P = 7500
Interest rate = 6%
3,150 = $7500 x 6% x t
3150 = $450 x t
3150/450 = t
7 = t
Gregory spent 7 years paying back his loan.
Turn and Talk Describe the key steps that were taken to solve the problem.
Check Understanding
Question 1.
Arisia puts $500.00 into a savings account with an annual simple interest
rate of 4.5%.
A. How much interest does she earn per year? ____
Answer:
Simple interest rate = PTR
Principal = P = $500.
Simple interest rate = 4.5%
Time = 1 year.
Simple interest rate = PTR = $500 x 4.5% x 1
= $2250
Interest she earns per year = $2,250.
B. If the interest rate stayed the same, how much interest would Arisia’s account earn after 15 years? ____
Answer:
Simple interest rate = PTR
Principal = P = $500.
Simple interest rate = 4.5%
Time = 15 year.
Simple interest rate = PTR = $500 x 4.5% x 15
= $33,750
Interest she earns per 15 years = $33,750.
C. If the interest rate stayed the same, how much money would be in Arisia’s account after 20 years? _____
Answer:
Simple interest rate = PTR
Principal = P = $500.
Simple interest rate = 4.5%
Time = 20 year.
Simple interest rate = PTR = $500 x 4.5% x 20
= $45000
Interest she earns per 20 years = $45000.
On Your Own
Question 2.
Model with Mathematics Write an equation to find the amount of interest $450,000 earns in 1 year at a simple interest rate of 3.5%.
___________
Answer:
Given that,
Principal P = $450,000.
Simple interest rate = $3.5%
Time = 1 year.
The equation to find the simple interest is PTR.
= $450,000 x 3.5% x 1
Simple interest I = $15,750
Question 3.
Marcus borrows $3,000 from his local credit union, to be repaid with 3.5% simple interest over 4 years. What are the principal, interest rate, and time in this situation?
Answer:
Given that,
Principal = $3,000
Simple interest rate = 3.5/100 = 0.035
Time = 4 years.
Question 4.
Inez opens a savings account with $2,400. The account pays her 2.4% annual simple interest.
A. Find the amount of simple interest that the account will earn per year.
Answer:
Given that,
Principal = $2,400
Simple interest rate = 2.4%
Time = 1 years.
Simple interest I = $2400 x 2.4% x 1
Simple interest I = $57.6
The simple interest that the account will earn per year is $57.6
B. Calculate the total interest Inez would earn in 10 years.
Answer:
Given that,
Principal = $2,400
Simple interest rate = 2.4%
Time = 1 years.
Simple interest I = $2400 x 2.4% x 10
Simple interest I = $576.
The simple interest that the account will earn per year is $576.
Total interest = $2400 + $576 = $2976.
The total interest Inez would earn in 10 years is $2976.
Question 5.
Green Bank has the ad shown. Barry opens a savings account after seeing the ad. He deposits $1,300.
A. Write an equation that relates the amount of time t in years that Barry holds his account to the amount of simple interest I that he earns.
Answer:
Given that,
Principal P = $1300
Interest rate = $2.2%
Time = t.
The equation for the simple interest is PTR
= $1300 x 2.2% x t
= $28.6t.
B. How much interest does Barry earn in 7 years?
________________
Answer:
The equation for the simple interest I = PTR.
Principal P = $1300
Interest rate = $2.2%
Time = 7 years
The equation for the simple interest is PTR
= $1300 x 2.2% x 7.
= $200.2
The interest Barry earns in 7 years is $200.2
C. At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300. What rate of simple interest is offered at the Blue Bank?
Answer:
The equation for the simple interest I = PTR.
Principal P = $1300
Interest rate = r%
Time = 7 years
Simple interest I = $159.25
The equation for the simple interest = PTR
$159.25 = $1300 x r% x 7.
$159.25 = $9100 x r%
$159.25/$9100 = r%
0.0175 = r%
1.75% = r
The rate of simple interest offered at the Blue Bank is 1.75%
Question 6.
Avram borrows $14,500 at 5.4% simple interest to open a small business. His bank allows him 9 years to pay back the loan.
A. How much simple interest will Avram have to pay on the loan?
Answer:
Given that,
Principal P = $14,500
Interest rate = 5.4%
Time = 9 years.
Simple interest = PTR.
Simple interest = $14,500 x 5.4% x 9
I = $7,047
The simple interest Avram will have to pay on the loan is $7,047.
B. How much money will Avram have to repay in all?
Answer:
Total money = P + I
Principal = $14,500
I = $7,047.
Total money = $14,500 + $7,047 = $21547
Avram has to repay all $21547.
Question 7.
Regina is buying a new car. She sees two advertisements in the paper for the same car at two different prices from two different dealerships. Both dealers are offering a simple-interest loan for the price of the car.
A. Regina calculates that to buy the car in Ad A, the loan would ultimately cost her $41,503. Over how many years is the loan in Ad A to be paid back?
Answer:
Given that,
Principal P = $24,200.
Interest rate = 6.5%
The loan cost = $41,503
Interest paid = $41,503 – $24,200 = $17303
The simple interest per 1 year = PTR
$24200 x 6.5% x 1 = $1573.
Number of years = $17303/$1573 = 11 years
The number of years the loan in Ad A to be paid back is 11 years.
B. Regina calculates that to buy the car in Ad B, the loan would ultimately cost her $38,402. What is the price of the car offered in Ad B?
Answer:
C. In either case, Regina would be paying back the dealer in equal monthly installments over the lifetime of the loan. What would her monthly payments be if she bought the car shown in Ad A?
_________________
What would her monthly payments be if she bought the car shown in Ad B?
Answer:
D. Open Ended In your opinion, which ad is offering the better deal? Explain why you think so.
_________________
Answer:
Question 8.
It costs $36,736 to repay a loan of $20,500 at 6.6% annual simple interest.
A. How much interest would you pay each year?
______________________
Answer:
Simple interest per 1 year = PTR
Principal = P = $20,500
Simple interest rate = 6.6%
Time = 1 year.
Simple interest I = $20,500 x 6.6% x 1
= $1353.
The simple interest per 1 year =$1353.
B. How many years does it take to repay the loan?
Answer:
Principal = P = $20,500
Simple interest rate = 6.6%
The simple interest per 1 year =$1353.
Time =?
Interest paid = $36736 – $20,500 = $16,236
Time = $16,236/$1353 = 12
The number of years it takes to repay the loan is 12 years.
Question 9.
A savings account pays an annual simple interest rate of 1.5%.
A. How much interest would you earn in 1 year on $2,000?
Answer:
Given that,
Principal = $2,000.
Interest rate = 1.5%
Time = 1 year.
Formula fo the simple interest I = PTR
I = $2000 x 1.5% x 1
= $30
The interest per 1 year = $30.
B. What would be the balance in your account after 5 years?
Answer:
Given that,
Principal = $2,000.
Interest rate = 1.5%
Time = 1 year.Formula fo the simple interest I = PTR
I = $2000 x 1.5% x 5
= $150
The interest per 5 years = $150.
The balance in your account after 5 years = $2000 + $150 = $2150.
C. How long would it take to earn $500 or more in interest?
Answer:
Given that,
Principal = $2,000.
Interest rate = 1.5%
Time = 1 year.
Formula for the simple interest I = PTR
I = $2000 x 1.5% x 1
= $30
The interest per 1 year = $30.
To earn 500 or more in interest = $500/$30 = 16.6
It means to earn 500 takes 16 years and 6 months.
Question 10.
A loan of $9,000 has an annual simple interest rate of 3.5%.
A. If you repay the loan in 6 years, how much total interest will you pay?
Answer:
Given that,
Loan = Principal P = $9000.
Simple interest rate = r = 3.5%
Time = 6 years
Simple interest I = PTR
= $9000 x 3.5% x 6
= $1890
Total interest = $1890
The total interest you will pay is $1890.
B. What is the total cost of the loan?
Answer:
Loan = Principal P = $9000.
Simple interest = $1890
Total cost = P + I
Total cost = $9000 + $1890 = $10890.
The total cost will be $10890.
C. What would be the simple interest rate if a loan of $9,000 that is repaid in 6 years has a total cost of $11,052?
Answer:
Loan = Principal P = $9000.
Total cost = $11,052
Amount of interest = PTR
$11052 = $9000 x 6 x t
$11052 = 54000 x t
$11052/$54000 = 0.204 = 20.4%
The simple interest rate if a loan of $9,000 that is repaid in 6 years has a total cost of $11,052 is 20.4%
Question 11.
A loan of $25,000 has an annual simple interest rate of 5.5%. The total cost of the loan is $38,750.
A. How much total interest will you pay?
Answer:
Given that,
Loan rate = $25,000
Simple interest rate = 5.5%
The total cost of the loan = is $38,750.
The total interest you will pay = $38,750 – $25,000.
= $13750.
The total interest you will pay is $13750.
B. How long does it take to repay the loan?
Answer:
Given that,
Loan rate = $25,000
Simple interest rate = 5.5%
Simple interest per 1 year = $25,000 x 5.5% x 1 = $1375.
The total interest you will pay is $13750.
$1375 x 10 = $13750.
He has to repay the loan for 10 years.
Lesson 2.5 Practice/Homework
Question 1.
Rena’s grandfather opened a savings account as a college fund for her. His initial deposit and the yearly simple interest rate are shown. How much will Rena have in this account after 2 years and 6 months?
Answer:
Given,
Initial deposit = $3500
SI = 3.25%
T = 4 years
SI = prt
I = 3500 × 3.25% × 4
I = 3500 × 3.25/100 × 4 = $455
Amount that will be in account after 4 years = $3500 + $455 = $3955
After 2 years 6 months
I = 3500 × 3.25% × 2.5
I = 3500 × 3.25/100 × 2.5 = $284.37
Amount that will be in account after 2 year 6 months = $3500 + $284.37= $3784.37
Question 2.
Big Money Bank has an offer for new customers: if you deposit $5,000 in a savings account, you will earn 6.5% simple interest over the first 10 years.
A. How much interest will the account earn over this period?
Answer:
I = Prt
P = 5000
r = 6.5%
t = 10
I = 5000 × 6.5% × 10
I = 5000 × 6.5/100 × 10
I = 10 × (5000 × 0.065)
I = 10 × 325 = 3250
Interest for 10 years = $3250
B. How much will be in the account after the 10-year period?
Answer:
C. At the Town Savings Bank, a new customer earns $2,950 in simple interest on a $5,000 deposit over the first 10 years. What rate of interest does that bank pay?
Answer:
At the Town Savings Bank, a new customer earns $2,950 in simple interest on a $5,000 deposit over the first 10 years.
The interest for 1 year
2950/10 = $295
The rate of interest
295/5000 × 100% = 5.9%
Question 3.
Dream Loan Bank offers loans. Carrie borrows $10,500 to help start a business. The loan must be repaid at 4.5% simple interest over 10 years. How much money will Carrie have to pay back?
Answer:
Given,
At the Town Savings Bank, a new customer earns $2,950 in simple interest on a $5,000 deposit over the first 10 years.
P = 10500
r = 4.5%
t = 10 years
F = P + Prt
F = 10500 + 10500 × 4.5/100 × 10
10500(1 + 0.45)
10500 × 1.45 = 15225
Carrie have to pay back $15225.
Question 4.
Financial Literacy Kevin is going to open a savings account with $4,000. Two different banks offer him two different options:
Bank A offers an account that will pay 6% simple interest for 6 years.
Bank B offers a special account for new customers that will pay 7% simple interest for 3 years. After the 3 years, Kevin would have to transfer all his earnings to a regular account that will pay 5% simple interest on the new transferred principal.
Which offer will leave Kevin with more money after 6 years? Explain.
Answer:
Given,
Kevin is going to open a savings account with $4,000.
Bank A offers an account that will pay 6% simple interest for 6 years.
4000 × 6% × 6
4000 × 6/100 × 6 = 1440
Second option:
4000 × 7% × 3 + 4000 × (7% × 3 + 1) × 5% × 3
= 840 + 4840 × 5% × 3
= 840 + 726
= 1566
1440 is less than 1556
Hence the second option will leave Kevin with more money after 6 years.
Test Prep
Question 5.
Delilah deposits $8,255 in an account that pays 4.2% simple interest. How much money will be in her account after 8 years?
A. $2,773.69
B. $11,028.68
C. $12,254.66
D. $27,736.80
Answer:
Given,
Delilah deposits $8,255 in an account that pays 4.2% simple interest.
P = 8255
T = 8 years
R = 4.2%
F = P(1 + Rt)
8255 (1 + (4.2%)8)
8255(1 + 0.336)
8255 × 1.336 = 11028.68
Thus option B is the correct answer.
Question 6.
Edgar takes out a loan of $5,540, to be repaid over 7 years at 8.5% Simple interest. How much interest will Edgar have to pay on the loan?
A. $470.90
B. $3,296.30
C. $3,775.60
D. $8,836.30
Answer:
Given,
Edgar takes out a loan of $5,540, to be repaid over 7 years at 8.5% Simple interest.
Simple Interest is the interest of each period that does not generate new interest.
5540 × 8.5% × 7 = 5540 × 85/10 × 7 = 3296.30
Thus option B is the correct answer.
Question 7.
Gregoria borrowed $2,450, to be paid back at 3.5% simple interest. She spent $3,221.75 in all to repay the loan. How many years did Gregoria take to repay the loan?
Answer:
Given,
Gregoria borrowed $2,450, to be paid back at 3.5% simple interest.
She spent $3,221.75 in all to repay the loan.
3221.75 – 2450 = 771.75
2450 × 35% = 2450 × 35/100 = 85.75
771.75 ÷ 85.75 = 9
Thus it takes 9 years to repay the loan.
Spiral Review
Use the number line shown for Problems 8 and 9.
Question 8.
What number is 3 units to the right of 2 on the number line?
_________________
Answer:
3 units to the right of 2 is 3 + 2 = 5
Question 9.
What number is 3 units to the left of 2?
_________________
Answer:
2 Units to the left of 3 is
3 – 2 = 1
Question 10.
Bianca had a weekly allowance of $8.50 two years ago. Last year, her weekly allowance was $9.75. This year, Bianca’s weekly allowance is $12.00. Does it make sense to represent the relationship between the amount of her allowance and the year with a constant rate? Why or why not?
_________________
Answer:
Given,
Bianca had a weekly allowance of $8.50 two years ago.
Last year, her weekly allowance was $9.75.
This year, Bianca’s weekly allowance is $12.00.
9.75 – 8.50 = 1.25
1.25/8.50 = 0.147 or 14.7 % increase
Between the second and third year, there was a change of
12 – 9.75 = 2.25 dollar change
2.25/9.75 = 0.23 or 23% increase
Hence, each year the percent and dollar value increase is increasing more and more which would not be a constant rate.