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Calculating Simple Interest Recall that the money you put in a savings account is called principal. The bank pays you interest at an agreed upon interest rate. Simple interest is interest paid only on the principal, and is paid out to the person who owns the account. It is not kept on deposit to earn more interest.

Roberto’s parents open a savings account for him on his birthday. The account earns simple interest at an annual rate of 5%. They deposit $100 and will deposit $100 on each birthday after that. Roberto will make no withdrawals from the account for at least 10 years. Make a table to show how the interest accumulates over five years.

Deposit phase

Beginning balance for new phase $

Amount deposited $

New balance $

Interest rate %

Amount of interest earned $

1 0 100 100 5 5

2 100 100 200 5 10

3 200 100 300 5 15

4 300 100 400 5 20

5 400 100 500 5 25

Total 75

Roberto earns a total of $75 in interest over the five years.

EXAMPLEXAMPLE 1

ESSENTIAL QUESTION

L E S S O N

13.2Calculating and Comparing Simple and Compound Interest

How do you calculate simple and compound interest?

Reflect1. Make a Prediction Predict how much simple

interest Roberto will have earned after the tenth year. Suppose he continues to make no withdrawals.

2. Each year Amy deposits $100 into an account that earns simple interest at an annual rate of 8%. How much interest will she earn over the first five years? How much will be in her account after that time?

YOUR TURN

Personal financial literacy—7.13.E Calculate and compare simple interest and compound interest earnings.

7.13.E

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Math On the Spotmy.hrw.com

Calculating Compound InterestMost banks pay compound interest. That is, interest earned is kept on deposit to earn more interest. Compound interest is computed on the entire amount in the account, including the principal, and any previously interest earned.

On Claudia’s birthday, her parents open a savings account and deposit $100. They also deposit $100 each year after that on her birthday. The account earns interest at an annual rate of 5% compounded annually. Claudia will make no withdrawals from the account for at least 10 years. Make a table to find the ending balance in Claudia's account after 5 years.

Deposit phase

Beginning balance for

new phase $

Amount deposited $

New balance $

Interest rate %

Amount of

interest earned $

Ending balance $

1 0.00 100 100.00 5 5.00 105.00

2 105.00 100 205.00 5 10.25 215.25

3 215.25 100 315.25 5 15.76 331.01

4 331.01 100 431.01 5 21.55 452.56

5 452.56 100 552.56 5 27.63 580.19

The total amount in the account at the end of the fifth year is $580.19.

Reflect3. Does the balance of Claudia’s account change by the same amount

each year? Explain why or why not.

4. Would the total amount in the account after 5 years be greater if the interest rate were higher? Explain.

EXAMPLE 2

5. What If? Suppose the interest rate on Claudia’s account is 6% instead of 5%. How much will Claudia have in her account at the end of the fifth year? How does it compare to the amount in Example 2?

YOUR TURN

The total amount in the account at the end of the fifth year is $580.19.

Math TalkMathematical Processes

7.13.E

How can you find the total amount of interest that

accumulates over the five years?

412 Unit 7

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Math On the Spot

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Animated Math

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Comparing Simple and Compound Interest You can use a formula for compound interest compounded annually to solve problems.

Jane has two savings accounts, Account S and Account C. Both accounts are opened with an initial deposit of $100 and an annual interest rate of 5%. No additional deposits are made, and no withdrawals are made. Account S earns simple interest, and Account C earns interest compounded annually. Which account will earn more interest after 10 years? How much more?

Find the total interest earned by Account S after 10 years.

Find the amount of interest earned in one year.

Principal × Interest rate = Interest for 1 year

$100 × 0.05 = $5

Find the amount of interest earned in ten years.

Interest for 1 year × Number of years = Interest for 10 years

$5 × 10 = $50

Account S will earn $50 after 10 years.

Find the final amount in Account C. Then subtract the principal to find the amount of interest earned.

A = P(1 + r)t

= 100 × (1 + 0.05)10

= 162.89

Account C will earn $162.89 - $100.00 = $62.89 after 10 years.

Compare the amounts using subtraction: $62.89 - $50 = $12.89

Account C earns $12.89 more in compound interest after 10 years than Account S earns in simple interest.

EXAMPLEXAMPLE 3

STEP 1

STEP 2

STEP 3

7.13.E

Use the compound interest formula.

Substitute 100 for P, 0.05 for r, 10 for t.

Calculate. Round to the nearest cent.

Compound Interest Compounded Annually

A = P(1 + r)t, where P is the principal (the original amount deposited), r is the interest rate expressed as a decimal, t is the time in years, and A is the amount in the account after t years if no withdrawals are made.

(1 + 0.05)10 means you have 10 factors of 1.05.

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6. What If? Suppose the accounts in Example 3 both have interest rates of 4.5%. Which account will earn more interest after 10 years? How much more?

YOUR TURN

Guided Practice

1. Each year on the same day, Hasan deposits $150 in a savings account that earns simple interest at an annual rate of 3%. He makes no other deposits or withdrawals. How much interest does his account earn after one year? After two years? After five years? (Example 1)

Keri deposits $100 in an account every year on the same day. She makes no other deposits or withdrawals. The account earns an annual rate of 4% compounded annually. Complete the table. (Example 2)

Deposit phase


Amount deposited $

New balance $

Interest rate %


Ending balance $

2. 1 0.00 100 100.00 4

3. 2 104.00 100 4

4. 3 100 4

5. 4 100 4

6. 5 100 4

7. Theo deposits $2,000 deposit in a savings account earning compound interest at an annual rate of 5% compounded annually. He makes no additional deposits or withdrawals. Use the formula for compound interest to find the amount in the account after 10 years. (Example 3)

8. Describe the difference between simple interest and compound interest.

ESSENTIAL QUESTION CHECK-IN???

414 Unit 7

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Name Class Date

Independent Practice13.2

Mia borrowed $5,000 from her grandparents to pay college expenses. She pays them $125 each month, and simple interest at an annual rate of 5% on the remaining balance of the loan at the end of each year.

9. How many months will it take her to pay the loan off? Explain.

10. For how many years will she pay interest? Explain.

11. How much simple interest will she pay her grandparents altogether? Explain.

12. Roman saves $500 each year in an account earning interest at an annual rate of 4% compounded annually. How much interest will the account earn at the end of each of the first 3 years?

13. Jackson started a savings account with $25. He plans to deposit $25 each month for the next 12 months, then continue those monthly deposits in following years. The account earns interest at an annual rate of 4% compounded annually, based on his final yearly balance. Fill in the chart to find out how much money he will have in the account after 3 years.

Deposit phase


Amount deposited by year end $

New balance $

Interest rate %


Ending balance $

1 25.00 300.00 325.00 4

2

3

7.13.E

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Work Area

14. Communicate Mathematical Ideas Look back at Exercise 13. Suppose Jackson increased the initial deposit by $75, but made the same monthly deposits. Would the balance at the end of every year increase by $75?

15. Account A and Account B both have a principal of $1,000 and an annual interest rate of 4%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?

16. Justify Reasoning Luisa deposited $2,000 in an account earning simple interest at an annual rate of 5%. She made no additional deposits and no withdrawals. When she closed the account, she had earned a total of $2,000 in interest. How long was the account open?

17. Draw Conclusions Amanda deposits $500 into a savings account earning simple interest at an annual rate of 8%. Tori deposits $1,000 into a savings account earning simple interest at an annual rate of 2.5%. Neither girl makes any additional deposits or withdrawals. Which girl’s account will reach a balance of $1,500 first? Justify your answer.

18. Persevere in Problem Solving Gary invested $1,000 in an account earning interest at an annual rate of 5% compounded annually. Each year, he deposited an additional $1,000, and made no withdrawals. When he closed the account, he had a balance of $4,525.64. Make a table similar to the one in Example 2 to help you estimate how long the money was in the account. How much interest would Gary earn in that same time if he invests $10,000 and deposits $10,000 into the account each year?

FOCUS ON HIGHER ORDER THINKING

416 Unit 7

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