managing your money chapter 10. earning interest
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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
win
g risk
to
inve
stor
’s c
apital
Increasing safety of
principal
Grow
ing risk of loss of
purchase power
Incr
easi
ng p
oten
tial
for
high
er ret
urns
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.
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