A Dollar Saved…Chapter 3

3-1 Savings

3-2 Compound Interest

3-3 The Federal Reserve

A Dollar Saved…Chapter 3

After completing this chapter, you should be able to• determine factors that affect returns on savings• compare types of and calculate interest on

savings accounts • identify the functions and policies of the Federal

Reserve • observe and calculate the multiplier effect on the

nation’s money supply

3-1 Savings: Save Now – Buy Later Warm-upWord Definition

Symbol/Formula

1. Bar graph

2. Certificate of Deposit

3. Commercial Banks

4. Credit Unions

5. Interest

6. Interest Rate

7. Liquidity

3-1 Savings: Save Now – Buy Later Warm-upWord Definition

Symbol/Formula

8. Money Market Account

9. Principal

10.Passbook/Regular Savings Account

11. Savings & Loan Associations

12. Savings Banks

13. Simple Interest

3-1 Savings: Save Now – Buy Later

Skill 1: Simple interestSimple Interest = prinicipal ∙ rate ∙ time

i = prt where i = interest

p = principal

r = interest rate

t = time

Total savings = weekly savings ∙ number of weeks

Balance = principal + interest B = p + i

3-1 Savings: Save Now – Buy Later Example

Maria can save $85 per week from her paycheck. After saving for a year, she decides to buy a one-year CD that pays 4% simple interest.

1. How much will Maria save in 52 weeks?

Total savings = weekly savings ∙ number of weeks

= 85 ∙ 52

= $4,420

3-1 Savings: Save Now – Buy Later

Example cont.Maria can save $85 per week from her paycheck. After saving for a year, she decides to buy a one-year CD that pays 4% simple interest.

2. How much interest will the CD earn in 1 year?

i = prt

i = 4420(4%)1

i = $176.80

3-1 Savings: Save Now – Buy Later

Example cont.Maria can save $85 per week from her paycheck. After saving for a year, she decides to buy a one-year CD that pays 4% simple interest.

3. How much will Maria’s CD be worth after 1 year?

B = p + i

B = 4420 + 176.80

B = $4596.80

3-1 Savings: Save Now – Buy Later Skill 2: Time needed to save money

Weeks needed

= cost of item ÷ amount saved each week

3-1 Savings: Save Now – Buy Later

ExampleMaria’s friend Dwight wants to buy a golf bag. He finds one on sale for $59.84. The sale price will be in effect for 1 month. If Dwight can save $22 per week, will he have enough money to buy the bag before the sale is over?

Weeks needed = cost ÷ amount saved

= 59.84 ÷ 22

= $2.72

≈ 3 weeks

Yes, he will be able to buy the golf bag before the sale ends.

3-2 Compound Interest: Money That Grows

Warm-upWord Definition

Symbol/Formula

1. Compound Interest

2. Compounded Quarterly

3. Compounded Semiannually

4. Rule of 72

3-2 Compound Interest: Money That Grows

Skill 1: Semiannual interestSemiannual Interest = prinicipal ∙ semiannual rate ÷ 2

i = pr/2 where i = interest

p = principal

r = interest rate

3-2 Compound Interest: Money That GrowsExample

Nelson’s parents have a CD in the amount of $10,000. It is held by a bank that pays 5% interest, compounded semiannually. How much will Nelson’s parents have in this account after 2 years?

i = pr/ 2

i = 10,000(5%)/2 i = 10,250(5%)/2

i = $250 (6mths) i = $256.25 (1yr)

i = 10,506.25(5%)/2 i = 10,768.91(5%)/2

i = $262.66 (1½ yr) i = $269.22 (2yrs)

After 2 years, there will be $11,038.13.

3-2 Compound Interest: Money That Grows

Skill 2: Compound interestCompound Interest B = p(1 + r)n

where B = balance

p = original principal

r = interest rate for the time period

n = total number of time periods

3-2 Compound Interest: Money That Grows

ExampleNelson’s parents have a CD in the amount of $10,000. It is held by a bank that pays 5% interest, compounded semiannually. How much will Nelson’s parents have in this account after 5 years?

B = p(1 + r)n

B = 10,000(1 + 5%/2)10

B = $12,800.85

3-2 Compound Interest: Money That Grows

Skill 3: Rule of 72Rule of 72

72/annual interest rate ∙ 100 = years to double

ExampleNelson invests $10,000 in a CD that pays 6%compounded quarterly. How long will it take his investment to double?

72/6% ∙100 = 12 years

3-3 The Federal Reserve: The Bank’s Bank

Warm-upWord Definition

Symbol/Formula

1. Common Ratio

2. Consumer Price Index

3. Easy-money Policy

4. Excess Reserves

5. Federal Reserve Note

6. Federal Reserve System

7. Geometric Series

3-3 The Federal Reserve: The Bank’s Bank

Warm-upWord Definition

Symbol/Formula

8. Inflation

9. Legal Tender

10.Money Supply

11.Multiplier Effect

12.Required Reserve

13.Sum of an Infinite Geometric Series

14.Tight-money policy

3-3 The Federal Reserve: The Bank’s Bank Skill 1: Multiplier effect

For demand deposits• Required reserve 20% • Loans and investments 80%

Loans and investments are redeposited in the banking system to create extra money or credit.

3-3 The Federal Reserve: The Bank’s Bank Example

Olivia wants to find out the multiplier effect on an initial deposit of $1000 through five levels. What is the total amount of extra money or credit created through five levels of the multiplier effect?

Original loans/investments = 1000(80%) = $800

Original reserve = 1000(20%) = $200

3-3 The Federal Reserve: The Bank’s Bank Example cont.

Level Demand Deposit

Reserve Loans/Investments

1 1000.00 200.00 800.00

2 800.00 800(20%) = 160.00 800-160 = 640.00

3 640.00 640(20%) = 128.00 640-128 = 512.00

4 512.00 512(20%) = 102.40 512-102.40 = 409.60

5 409.60 409.60(20%) = 81.92 409.60-81.92 = 327.68

Total money created = $2689.28

3-3 The Federal Reserve: The Bank’s Bank Skill 2: Sum of an infinite geometric seriesSum of an Infinite Geometric Series

S = a where S = sum of the series

1 – r a= the 1st term in the series

r = the common ratio (0.8)or

Multiplier = original deposit + sum of the series

original deposit

3-3 The Federal Reserve: The Bank’s Bank Example

Olivia wants to find out the maximum multiplier effect on an initial deposit of $1000. What is the maximum amount of money his deposit can create and what is the multiplier?

S = a Multiplier = 1000 + 40001 – r 1000

= 800 = 5

1 – 0.8

S = $4000