Financial Algebra© Cengage/South-Western Slide 11

BANKING SERVICES

BANKING SERVICES

3-1 Checking Accounts

3-2 Reconcile a Bank Statement

3-3 Savings Accounts

3-4 Explore Compound Interest

3

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BANKING SERVICES BANKING SERVICES

3-5 Compound Interest Formula

3-6 Continuous Compounding

3-7 Future Value of Investments

3-8 Present Value of Investments

3

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3-3

SAVINGS ACCOUNTS3-3

SAVINGS ACCOUNTS

Learn the basic vocabulary of savings accounts.

You will be able to compute simple interest using the simple interest formula.

OBJECTIVES

Financial Algebra© Cengage Learning/South-Western Slide 44

savings account interest interest rate* principal* simple interest* simple interest formula*

statement savings minimum balance* money market account* certificate of deposit

(CD)* maturity*

Key Terms

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What types of savings accounts do What types of savings accounts do banks offer customers?banks offer customers?What types of savings accounts do What types of savings accounts do banks offer customers?banks offer customers?

What banking services does your family use?Where does the money that banks lend out for

loans come from?What is the value of compound interest?What are the advantages of direct deposit?

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Grace wants to deposit $5,000 in a certificate of deposit for a period of two years. She is comparing interest rates quoted by three local banks and one online bank. Write the interest rates in ascending order. Which bank pays the highest interest for this two-year CD?

First State Bank: 4 % E-Save Bank: 4 %

Johnson City Trust: 4.22% Land Savings Bank: 4.3%

3

8

1

4

Example 1Example 1Example 1Example 1

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First State Bank: 4 % E-Save Bank: 4

Johnson City Trust: 4.22% Land Savings Bank: 4.3%

3

8

1

4

Example 1 (cont.)Example 1 (cont.)Example 1 (cont.)Example 1 (cont.)

•Change fractions to decimals.4 = 4.25 4 = 4.3751

4

3

8

•Add zeroes so they all have the same number of decimal places.

4.250 4.375 4.220 4.300•Write the original numbers in order.

4.22% 4 % 4.3% 4 %1

4

3

8

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Write the following five interest rates in descending order (greatest to least):5.51%, 5 %, 5 %, 5.099%, 5.6%1

2

5

8

CHECK YOUR UNDERSTANDING

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Example 2Example 2Example 2Example 2

Raoul’s savings account must have at least $500, or he is charged a $4 fee. His balance was $716.23, when he withdrew $225. What was his balance?

• Subtract the withdrawal. 716.23 – 225 = 491.23• Compare to the minimum. 491.23 < 500• Subtract the penalty. 491.23 – 4 = 487.23

Raoul’s balance was $487.23

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Mae has $891 in her account. A $7 fee is charged each month the balance is below $750. She withdraws $315. If she makes no deposits or withdrawals for the next x months, express her balance algebraically.

CHECK YOUR UNDERSTANDING

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EXAMPLE 3EXAMPLE 3EXAMPLE 3EXAMPLE 3

Mitchell deposits $1,200 in an account that pays 4.5% simple interest. He keeps the money in the account for three years without any deposits or withdrawals. How much is in the account after three years?

• Use the simple interest formula. I = prt• Express the interest as a decimal

I = 1200 • 0.045 • 3 = 162• Add the interest and principal 162 + 1200 = 1362The balance after three years is $1,362.

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How much simple interest is earned on $4,000 in 3½ years at an interest rate of 5.2%?

CHECK YOUR UNDERSTANDING

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EXAMPLE 4EXAMPLE 4EXAMPLE 4EXAMPLE 4

How much simple interest does $2,000 earn in 7 months at an interest rate of 5%?

• Use the simple interest formula. I = prt• Change 5% to a decimal. r = 0.05

• Change 7 months to years. t = years12

7

• Substitute and simplify. I = 2000 • 0.05 •

58.33

12

7

The account earns $58.33.

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How much simple interest would $800 earn in 300 days in a non-leap year at an interest rate of 5.71%? Round to the nearest cent.

CHECK YOUR UNDERSTANDING

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EXAMPLE 5EXAMPLE 5EXAMPLE 5EXAMPLE 5

How much principal must be deposited to earn $1,000 simple interest in 2 years at a rate of 5%?

• Solve the simple interest formula for p.

• A principal of $10,000 must be deposited

prtI

prt

I

rt

prt

rt

I

000,10205.0

000,1

p

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How much principal must be deposited in a two-year simple interest account that pays 3¼% interest to earn $300 in interest?

CHECK YOUR UNDERSTANDING

Financial Algebra© Cengage Learning/South-Western

Derek has a bank account that pays 4.1% simple interest. The balance is $910. When will the account grow to $1,000?

• We know: r = 4.1% = = 0.041 p = 910 and I = 1000 – 910 = 90

• Solve the simple interest formula for t.

His account will grow to $1,000 in approximately 2.4 years.

Slide 1717

EXAMPLE 6EXAMPLE 6EXAMPLE 6EXAMPLE 6

100

1.4

prtI

pr

prt

pr

I

tpr

I4.2

041.0910

90

t

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How long will it take $10,000 to double at 11% simple interest?

CHECK YOUR UNDERSTANDING

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EXAMPLE 7EXAMPLE 7EXAMPLE 7EXAMPLE 7 Kerry invests $5,000 in a simple interest account for 5 years.

What interest rate must the account pay so there is $6,000 at the end of 5 years?

• The interest is 6000 – 5000 = 1000• Solve the simple interest formula for r.

• The account must pay 4% annual simple interest.

prtI

pt

prt

pt

I

rpt

I

04.055000

1000

r

Financial Algebra© Cengage Learning/South-Western Slide 2020

Marcos deposited $500 into a 2.5-year simple interest account. He wants to earn $200 interest. What interest rate must the account pay?

CHECK YOUR UNDERSTANDING