managing your money chapter 10. earning interest

Managing Your MoneyChapter 10

Earning Interest

How Your Money Grows

Principal – amount of money deposited by a saver

Interest - money paid for the use of money; earnings on a savings acct.

Compound Interest – interest computed on the original principal plus the accumulated interest

Compound Interest

Interest can be compounded daily, monthly, or annually.

Not all savings accounts are created equal! Let’s see why.

Three factors affecting the time value calculations

TimeAmount invested Interest rate

Time value of money

Time value of money -- Money to be paid out or received in the future is not equivalent to money paid out or received today.

Compounding interest

Compounding interest -- Earning interest on interest.

“Make your money work for you.” Developed because compounding

interest causes money to make money.

$1,000 Invested Compounded Annually at 10% Interest Rate

1 Year 2 Years

$1,104.71 $1,220.39

Simple interest

Simple interest -- Interest earned on the principal investment. Principal -- The original amount of money

invested or saved. Amount invested x annual interest rate x

number of years = interest earned. Ex. 1,000 x 0.10 x 2=$200

$1,000 Invested at 10% Simple Interest Rate

1 Year 2 Years

$1,100.00 $1,200.00

Time

The earlier an individual invests, the more time their investment has to compound interest and increase in value.

A little goes a long way

Sally Saver puts away $3,000 per year in her IRA account earning 10% - she does this for 10 years then stops

Sally accumulates $1,239,564 by the age of 65.

Ed Uninformed waits until he is 28. He must contribute $3,000 to his IRA account earning 10% for 38 years.

Ed accumulates $1,102,331 by the age of 65.

Amount invested

Investing only a small amount a month is better than not investing at all.Ex. At 8% interest, invested at age 17,

one dollar per day will become $17,865.52 by age 65.

The larger the amount invested the greater return a person will earn.

Always pay yourself first.Savings should be a fixed expense.

Amount invested continued

70-20-10 Rule70% Spent20% Saved10% Invested

Flexible expenses can be decreased in order to increase the amount a person is able to invest.

The costs add up

Item Average Yearly Expense

Future Value

Eating lunch out 5 days per week at a cost of $5-$10 each time

$1,300.00-$2,600.00 $55,140.60 - $110,281.21

Daily candy bar $365.00 $15,481.78

Monthly gym membership at $38.00

$456.00 $19,341.63

Monthly hair cut at $25.00 per month

$300.00 $12,724.75

The future value problems are calculated for an 18 year old person investing at 8% until age 65.

Interest rate

The percentage rate paid on the money invested or saved.

Higher interest = more money earned

$1,000 Invested Compounded Monthly

Interest Rate

1 Year 5 Years 10 Years

4% $1,040.74 $1,221.00 $1,490.83

6% $1,061.68 $1,348.85 $1,819.40

Risk

A higher interest rate generally has a greater risk.Risk -- The uncertainty of the

outcome of an investment.

Fixed interest rate

Fixed interest rate -- The rate will not change for the lifetime of the investment.

Having a savings or investment plan with a fixed interest rate guarantees a specific return but can provide a moderate risk.

If the average interest rates rise, the amount a person earns from this type of investment will not increase.

Inflation

Another consideration with interest rates is ensuring the interest rate is higher than the rate of inflation.Inflation -- The steady rise in the

general level of prices.Ex. If an individual has money

invested at 4% interest and the inflation rate is 4%, the individual’s wealth will stay the same.

Time value of money calculations I = PRT

Present value PV=(FV)(1+i)-N

Future value FV=(PV)(1+i)N

Step 1: Principal X Interest Rate (in decimal form) X Time

Periods = Interest Earned Step 2: Principal + Interest Earned = Amount Investment is

Worth

Simple Interest Example

$1,000. at 5% for 3 years

$1,000 x .05 x 3 = $150.00 interest

$1,000 + $150 = $1,150.00

Compound Interest Example

$1,000. at 5% for 3 years

$1,000. x .05 x 1 = 50.00

$1,050. x .05 x 1 = 52.50

$1,102.50 x .05 x 1 = 55.13

$1,157.63 ($157.63 interest )

Calculation components

Present value (PV) -- How much money a person has today.

Future value (FV) – How much money a person expects to have in the future.

Interest rate (i) – The percentage rate paid on the money invested or saved.

Time (N) -- Length of investmentCalculated by the number of compounding

periods. (daily, monthly, or annually)

Review

Compounding interest earns interest on interest.

Increased time=more interest earned

Higher principal=more interest earned

Higher interest rate=more interest earned

What would you do?

$100.00 Invested at an 8% interest rate

Age Amount Earned

17 $100.00

25 $189.25

35 $420.06

45 $932.38

55 $2,069.54

65 $4,593.63

If participants choose to invest the money into an account earning 8% interest compounded annual at age 17 and leave the money invested until age 65, they will earn $4,593.63.

What would you do?

$100.00 Invested at an 8% interest rate

Age Amount Earned

17 $30.00

25 $56.77

35 $126.02

45 $279.71

55 $620.86

65 $1,378.09

What if the participant chooses to invest $30.00?

Compound Interest5 Years 10 Years

No Interest $1,000. $1,000.

Annual Compounding at 5%

$1,276. $1,629.

Monthly Compounding at 5%

$1,283. $1,647.

Daily Compounding at 5%

$1,284. $1,649.

Saving $1 a DayNo Interest 5% Daily

Compounding

Year 1 $365 $374

Year 5 $1,825 $2,073

Year 10 $3,650 $4,735

Year 30 $10,950 $25,415

How your money grows

Earnings on savings can be measured by the rate of return or yield

YIELD – percentage of increase in the value of your savings due to earned interest (APY)

--takes compounding into consideration also allows consumers to compare rates among banks

Rule of 72

72 = Years to

Interest Rate

double investment (or debt)

The answers can be easily discovered by knowing the Rule of 72The time it will take an investment

(or debt) to double in value at a given interest rate using compounding interest.

Albert Einstein

“It is the greatest mathematical

discovery of all time.”

Credited for discovering the mathematical equation for

compounding interest, thus the

“Rule of 72”

T=P(I+I/N)YN

What the “Rule of 72” can determine

How many years it will take an investment to double at a given interest rate using compounding interest.

How long it will take debt to double if no payments are made.

The interest rate an investment must earn to double within a specific time period.

How many times money (or debt) will double in a specific time period.

Things to Know about the “Rule of 72”

The “Rule of 72”Is only an approximationThe interest rate must remain

constantThe equation does not allow for

additional payments to be made to the original amount

Interest earned is reinvestedTax deductions are not included

within the equation

Doug’s Certificate of Deposit

Invested $2,500 Interest Rate is 6.5%

72 = 11 years to double investment

6.5%

Doug invested $2,500 into a Certificate of Deposit earning a 6.5% interest rate. How

long will it take Doug’s investment to double?

Another Example

The average stock market return since 1926 has been 11%

Therefore, every 6.5 years an individual’s investment in the

stock market has doubled

72 = 6.5 years to double investment

11%

Jessica’s Credit Card Debt

$2,200 balance on credit card18% interest rate

72 = 4 years to double debt18%

Jessica has a $2,200 balance on her credit card with an 18% interest rate. If Jessica chooses to not make any payments and does not receive late charges, how long

will it take for her balance to double?

Another Example

$6,000 balance on credit card22% interest rate

72 = 3.3 years to double debt

22%

Jacob’s Car

$5,000 to investWants investment to double in 4

years72 = 18% interest rate

4 years

Jacob currently has $5,000 to invest in a car after graduation in 4 years. What interest

rate is required for him to double his investment?

Another Example

$3,000 to investWants investment to double in

10 years

72 = 7.2% interest rate10 years

Rhonda’s Treasury Note

72 = 9.6 years

7.5% to double investment

Age Investment

22 $2,500

31.6 $5,000

41.2 $10,000

50.8 $20,000

60.4 $40,000

70 $80,000

Rhonda is 22 years old and would like to invest $2,500 into a U.S. Treasury Note earning 7.5%

interest. How many times will Rhonda’s investment double before she withdraws it at age 70?

Another Example

$500 invested at age 18 7% interest How many times will investment double

before age 65?

72 =10.2 years

7% to double investment

Age Investment

18 $500

28.2 $1,000

38.4 $2,000

48.6 $4,000

58.8 $8,000

69 $16,000

Taxes

A person can choose to invest into two types of accounts:

Taxable Account – taxes charged to earned interest

Tax Deferred Account – taxes are not paid until the individual withdraws the money from the investment

Taxes Example

George is in the 33% tax bracket. He would like to invest $100,000.

George is comparing two accounts that have a 6% interest rate. The first is a taxable account charging

interest earned. The second account is tax deferred until he withdraws the

money. Which account should George invest his money into?

Effects of taxes

Years Taxable Tax Deferred

12 $200,000

18 $200,000

24 $400,000

36 $400,000 $800,000

Taxable Account Earning 4% after taxes

72 =18 years

4% to double investment

Tax Deferred Account

72 = 12 years

6% to double investment

Conclusion

The Rule of 72 can tell a person:How many years it will take an

investment to double at a given interest rate using compounding interest;

How long it will take debt to double if no payments are made;

The interest rate an investment must earn to double within a specific time period;

How many times money (or debt) will double in a specific time period.

Conclusion continued

Things individuals must remember about the Rule of 72 include:Is only an approximationThe interest rate must remain constantThe equation does not allow for additional

payments to be made to the original amount

Interest earned is reinvestedTax deductions are not included within

the equation

WHERE You Can SAVE

COMMERCIAL BANKS-- widest variety of banking services Checking Savings ATM’s Overdraft

protection LoansAlmost all insured by FDIC

FDIC

The standard insurance amount of $250,000 per depositor is in effect through December 31, 2013. On January 1, 2014, the standard insurance amount will return to $100,000 per depositor for all account categories except IRAs and other certain retirement accounts, which will remain at $250,000 per depositor.

WHERE You Can SAVE

SAVINGS BANKSUsually referred to as mutual savings banks

- fewer in number Savings Real Estate Loans Home-improvement Loans Checking accounts

WHERE You Can SAVE

SAVINGS & LOAN ASSOCIATIONS

Organized primarily to lend money for home mortgages

Checking accounts Special Savings Business loans ATM’s / credit cards Many today have merged with Banks

WHERE You Can SAVE

CREDIT UNIONSNot-for-Profit organizations

established by groups of employees in similar occupations who pool their money

-- higher interest rates on savings-- lower interest rates on loans-- IRA’s-- checking accounts, CD’s

WHERE You Can SAVE

CREDIT UNIONSOwned by their members – must

be a member of the groupSHARE ACCOUNT – savings

account at a credit unionProvides insurance up to

$100,000

New NCUA Rules for Insurance CoverageTemporary increase in basic NCUA insurance amount

Effective October 3, 2008, the basic limit on federal share insurance coverage has been temporarily increased from $100,000 to $250,000 per member. The legislation provides that the basic share insurance limit, or standard maximum share insurance amount, for most types of accounts will return to $100,000 after December 31, 2013.

WHERE You Can SAVE

BROKERAGE FIRMS

SECURITIES – stocks, bonds issued by corporations or by the gov’t.

STOCKS = equity BONDS = debt

STOCKBROKER – a licensed employee of a brokerage firm who buys/sells securities for investors

SAVINGS OPTIONSREGULAR SAVINGS ACCOUNT

Major advantage - high liquidityfree to make deposits/withdrawalsATM card available

LIQUIDITY – ability of an asset to be converted into cash quickly without loss of value

Disadvantage - pays least amount of interest of the savings optionsMonthly fee assessed if balance falls below a minimum

amount

WHERE You Can SAVE

CERTIFICATE OF DEPOSIT (CD)

a/k/a time deposit – earns a fixed interest rate for a specified length of time

-- requires a minimum deposit-- interest rate slightly higher than

Savings (less liquid)-- penalty for early withdrawal

Cash ManagementThe daily routine of handling

money to take care of individual or family needs

Cash Management

Cash Management

Effective cash management includes having available money for:

Living expensesEmergenciesSavingsInvesting

Cash Management Tool

Cash Management ToolA financial account used to assist

with daily cash management

Checking AccountTool used to transfer funds

deposited into an account to make a cash purchase

Checking accounts may be non-interest or interest earning

Checking Account

Funds are easily accessed by: Checks Automated teller machines (ATMs) Debit cards Telephone Internet

Features may include: Minimum balance requirements Charge transaction fees Limited number of checks

written monthly Reduces the need to carry large amounts of

cash

Checking Account continued

Savings Account

Savings Account Account to hold money not spent on

consumption Interest bearing Have a lower interest rate than

other cash management tools Money may be accessed or transferred

between accounts through: Automated teller machines Telephones Internet

Savings Account continued

Features may include:Allows for frequent deposits or

withdrawalsEasily accessibleMoney storage for emergencies or

daily livingAvailable at depository institutionsMay require a minimum balance or

have a limited number of withdrawals

Money Market Deposit Account

Money Market Deposit Account A government insured account offered

at most depository institutionsHave a minimum balance requirement

with tiered interest ratesThe amount of interest earned depends

on the account balance For example: a balance of $10,000

will earn a higher interest rate than a balance of $2,500

Money Market Deposit Account continued

Accessibility is usually limited to three to six transactions each month

Features of may include:Minimum amount required to open the

account, often $1,000If the average monthly balance falls

below a specified amount, the entire account will earn a lower interest rate

Checks written – minimum $250.00

Certificate of Deposit (CD)

Certificate of Deposit (CD)An insured, interest earning

savings instrument with restricted access to the funds

Found in depository institutions accepting deposits for a certain length of time

Interest rates vary depending upon specified time length

The longer the length, the higher the interest rate

Certificate of Deposit continued

Features may include:Range from seven days to eight years in

lengthMinimum deposits range from $100-

$100,000If funds are withdrawn before the

expiration date, penalties are assessedLow risk and no fees

Savings Bond

Savings Bond Discount bond purchased for 50% of

the face value from the U.S. Government

Interest earned on a bond is tax exempt until redeemed. No taxes are due on interest earned It will be tax exempt when redeemed if

used for college expenses

Savings Bond continued

Access to funds is restrictedFeatures of may include:

Many different types availableCan be purchased for $25.00 -

$10,000.00A $100.00 bond would be purchased

for $50.00. When the bond matures to $100.00, it can be redeemed

Cash Management ToolsTool

Average Interest Earned

Purchase Place Special Features

Checking Account

1.5%

Commercial Banks, Savings & Loan Associations, Credit Union

Can be used in place of cash, funds can be easily accessed

Savings Account

2.3%

Commercial Banks, Savings & Loan Associations, Credit Union

Easily accessed, temporary holding place for funds

Money Market Account

2.6%

Commercial Banks, Savings & Loan Associations, Credit Union

Minimum balance, limited transactions, tiered interest rates

Certificate of Deposit

4.0% - 5.4%, depending on the length of deposit

Commercial Banks, other institutions which accept deposits for a fixed period

Penalties for early withdrawals, no deposits or withdrawals are made after initial investment

Savings Bonds

4.0% - 5.4%, depending on the length of bond

Commercial Banks, Credit Unions, employer payroll deduction plans

Tax advantages, a loan to the federal government

Liquidity

How quickly and easily an asset can be converted into cash

Investors should:Invest in both liquid and non-liquid toolsLiquid assets are important for

emergencies when cash must be quickly accessed

Cash management tools are protected by the U.S. Government against loss

Liquidity

Liquidity

Checking Account

Savings Account

Money Market Deposit Account

Certificate of Deposit

Savings Bond

Most Liquid

Least Liquid

Low Risk

These five cash management tools are low risk:Insures the funds so the

consumer does not lose money on the investment

However, they have lower interest ratesCauses low returns

Investment Risk PyramidGro

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Increasing safety of

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Grow

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Summary

Cash management is a daily routine of handling money to have enough funds for: Living expensesEmergenciesSavingsInvesting

Summary

Five types of cash management tools:

Checking accountSavings accountMoney market deposit accountCertificate of depositSavings bond

What are some personal factors that help determine the amount of money you will save?NAME 4

(a) amount of discretionary income,

(b) the importance you attach to savings,

(c) anticipated wants and needs, (d) will power or ability to forego

present spending in order to provide for your future

Why might people choose to save their money in a commercial bank when another type of financial institution offers a higher interest rate?

People choose commercial banks mainly because of the many services they offer

C O N V E N I E N C E !

 Is a credit union “for profit” or “not for profit”?

Credit unions are not-for-profit organizations established by groups of employees in similar occupations who pool their money.

Why types of loans do savings and loan associations primarily provide for their customers?

Savings and loan associations are organized primarily to lend money for home mortgages.

How much is an account insured for by the FDIC?

Accounts are insured for up to $250,000 per depositor per financial institution

Why does a regular savings account pay less interest than a certificate of deposit?

A regular savings account has complete liquidity; therefore, the interest rate is low.

What FOUR (4) things should you consider when choosing a financial institution for your savings?

(a) safety, (b) liquidity, (c) convenience, (d) interest earning

Describe two (2)  ways you can force yourself to save.

(a) automatic deductions (b) savings clubs

If two savings accounts offered 5 percent interest, but one was compounded quarterly and other was compounded daily, which account would have the higher APY?

The more often interest is compounded, the greater your earnings. You earn more interest with quarterly compounding than with annual compounding, and more interest with daily compounding than with quarterly compounding.