Savings AccountsSection 3.3

What is a savings account?

• An account in which the bank pays interest for the use of money deposited.

• Bank then uses that money to give loans.

• Charges a greater interest rate on that loan allowing the bank to pay you interest and still make money.

Types of Accounts

• Savings Account– Pays interest, may be a minimum balance,

unlimited access to money• Money Market Account

– Interest rate is higher, must have minimum amount in account, unlimited access to money

• Certificate of Deposit (CD)– Highest interest rate, do not have access to money

until certificate matures (expires)

Think about it…

• Is there a risk in putting money into a savings account?• The FDIC guarantees the safety of money in a bank up to

$250,000

• During the Great Depression, this was not the case

Grace just received a sum of $5,000 for her middle school graduation. She decides that she wants to put the money away for a period of 3 years so that she can put it towards a car. However, Grace is not sure what type of account she should put it in. What do you think?

Savings, Money Market, CD, Checking

Grace is going to deposit $5,000 into a CD for a period of 2 years. She is comparing interest rates quoted by 3 local banks and 1 online bank. Write the interest rate in ascending order. First State Bank: 4 ¼ % E-Save Bank: 4 %

Johnson Trust: 4.22% Land Bank: 4.3%

83

4.25% 4.375%

4.22% 4.3%

Ascending Order: 4.22% 4 ¼ % 4.3% 4 %83

Write the following five interest rates in descending order (greatest to least)

5.51 % 5 ½ % 5 % 5.099% 5.6%5.5% 5.625%

Descending Order:

85

5.099%

5 %85

5.6%5.51%5 ½ %

Minimum Balance Fee

• Banks can charge you a fee if you fail to keep a minimum amount of money in your account

• Makes it important to keep an accurate check register

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 is his new balance?

Balance after withdrawal: 716.23 – 225 = $491.23

Since this is less than $500, he is charged an additional $4

= 491.23 – 4= $487.23

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.

Balance after withdrawal: 891 – 315 = $576

Since this is less than $750, he is charged an additional $7 for every month.

Total fee of 7x= 576 – 7x

Class Work

• Page 135, numbers 2-6

SIMPLE INTEREST

What is interest?

• A sum paid or charged for the use of borrowing money.

2 Types of Interest

• Simple Interest– Interest is calculated only on principal

• Compound Interest– Interest is calculated on principal and interest– Increases the total principal

Simple Interest Formula

I = P r tI =

P =

r =

t =

Using the simple interest formula

1) Write the formula

2) Substitute values for variables

3) Solve the equation for the unknown variable

4) Answer the question

Converting time to years

• If given:

Months:

Weeks:

Days:

9 months:

27 weeks:

245 days:

Divide by 12

Divide by 52

Divide by 365

0.75 yrs

0.519 yrs

0.671 yrs

How much simple interest is earned on $4,000 in 3 ½ years at an interest rate of 5.2%.

I = P r t

I = Principal rate time $4,000 0.052 3.5 years

I = $728

$728 was earned in interest

1) Write the formula

2) Substitute values for variables

3) Solve for the unknown variable

4) Answer the question

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?

I = P r tI = P = r =

t =

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

How much simple interest would $800 earn in 300 days in a non-leap year at an interest rate of 5.71%?

SIMPLE INTEREST

Simple Interest Formula

I = P r tI =

P =

r =

t =

Interest earnedPrincipal (money invested)Annual interest rate (decimal)

Time (in years)

I = P r t

• So far, we have been solving problems to find the interest earned

• Now want to use this formula to solve for principal, rate, and/or time

• Can also use magic triangle

Magic Triangle

I

P r t

To solve an equation for a specific variable, simply cover the letter with your hand.

Find Principal:Find Rate:Find Time:rt

I

Pt

I

Pr

I

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

1. Use the triangle to find the formula

I

P r t

Principal =rt

I

205.0

000,1

= $10,000

$10,000 must be deposited to earn $1,000 in interest

How much principal must be deposited in a 2-year simple interest account that pays 3 ¼ % interest to earn $300?

Use the triangle to find the formula

I

P r t

Principal =rt

I

20325.0

300

= $4,615.38

$4,615.38 must be deposited to earn $300 in interest

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

How much do you need to earn in interest?

I

P r t

Time =Pr

I041.0910

90

= 2.2

In 2.2 years, the balance will reach $1,000

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

How much do you need to earn in interest?

I

P r t

Time =Pr

I

11.0000,10

000,10

= 9

It will take approximately 9 years to double.

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?

What are we looking for?

I

P r t

Rate =Pt

I

5000,5

000,1

= 0.04

She will need an interest rate of 4%.

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

I

P r t

Rate =Pt

I

5.2500

200

= 0.16

He will need an account that pays 16%.

How much simple interest is earned on $5,000 deposited in an account that earns 3% interest if it is left there for 5 years?

How much money would need to be deposited to earn $350 in interest at 3% for 6 years?

What interest rate would you need for $5,000 to grow to $5,750 in 4 years?

How long will it take $5,000 to double in an account that pays 5.6% simple interest?