Compound interest.

```All I can do is remind them of the truth of Albert
Einstein’s alleged response when he was asked,
“What do you, Mr. Einstein, consider to be man’s
greatest invention?” He didn’t reply the wheel or
the lever. He is reported to have said,
“Compound interest.”
1
Insured Accounts
Consumer Math 2012-2013
2
Overview
• Differences between checking and savings
accounts
• APR vs. APY
• CDs
• MMAs
• Simple Interest
• Compound Interest
3
• Interest Earned
Differences
– Savings: All earn interest
– Checking: Few earn interest (if you meet requirements)
• Number of Transactions
– Savings: Unlimited deposits, 3-6 withdrawals a month
– Checking: Unlimited deposits/withdrawals
• Funds Access
– Savings: Limited (in person or online transfers from one account to another)
– Checking: Convenient (ATMS, in person, or online)
• Fees
– Savings: None (if monthly withdrawals don’t go over limit)
– Checking: Overdraft fees, minimum balance fees, ATM fees, Online Access
fees, Bill Pay fees
• Bill Paying
– Savings: Not usually offered with online services
– Checking: Automatic withdrawals to pay loans, credit cards, gym
memberships or other ongoing expenses. Single withdrawals too.
4
Interest
• Money you receive from a bank or institution
for storing your money (principal) with them
– APR (Annual Percentage Rate)
– APY (Annual Percentage Yield)
5
APR vs APY
• APR
– APR is the annual rate of interest without taking into
account the compounding of interest within that year.
–
• APY
– APY does take into account the effects of intra-year
compounding.
Online APR -> APY Calculator http://instacalc.com/4968
6
Example 1
• If your credit card company charges 1% a
month APR, what % is that a year?
APR = 1% x 12
APR = 12% per year
7
Example 2
• If your credit card company charges 1% a
month APY, what % is that a year?
APY = (1+.01%)^(12)-1
APY = 12.68%
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Lesson 4 End
• Review
• Quiz
9
Simple Interest
A=P+PxRxT
• Simple Interest
– Money you receive solely based off of a principal
amount
•
•
•
•
•
A = Final amount
I = Interest Earned
Principle = original invested amount
R = % Rate (as a decimal)
T = Time in years
10
Example 3
• Your bank with pay you 2.1% APR simple
interest per year. You deposit \$3,050 in your
savings account in January.
– How much interest will you have earned in 1 year?
– What is the total amount in your savings account?
Interest = 3,050 x 0.021 x 1 = 64.05
Total Amount = 3,050 + 64.05 = 3,114.05
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Example 4
• You have a choice between 3 bank accounts.
Which one should you choose to make the most
simple interest?
1. Principle = \$1,200, Rate = 3%, Time = 3 years
2. Principle = \$1,200, Rate = 2%, Time = 4 years
3. Principle = \$1,200, Rate = 5%, Time = 2 years
1. 1200 x .03 x 3 = \$108
2. 1200 x .02 x 4 = \$96
3. 1200 x .05 x 2 = \$120
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Compound Interest
• Compound Interest
– Money you receive based off of a principal amount and
• Formula for annual compound interest
A = final amount
P = original invested amount (principal)
r = annual % rate (APR as a decimal)
t = number of years
n = number of times the interest is compounded per year
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Principle = \$1,000 & APR = 10%
• Simple Interest (Non-compounding):
Year 1
Year 2 Start
Year 3 Start
Year 4 Start
\$1,000
\$1,100
\$1,200
\$1,300
Interest on \$1000
= \$100
Interest on \$1000
= \$100
Interest on \$1000
= \$100
• Compound Interest (Annual Compounding):
Year 1
Year 2 Start
Year 3 Start
Year 4 Start
\$1,000
\$1,100
\$1,210
\$1,331
Interest on \$1000
= \$100
Interest on \$1,100
= \$110
Interest on \$1,210
= \$121
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Simple vs. Compound
•
•
•
•
Principal = \$2,000
Rate = 5%
Time = 6 years
Compounded Annually
Simple Interest
A = 2000+2000 x .05 x 6
A = \$2,600
Compounded Interest
A = 2000(1+(.05/1))^(1*6)
A = \$2,680.19
15
16
Compound Interest Calculator
http://www.ultimatecalculators.com/future_val
ue_annuity_calculator.html
• Retirement Time Horizon:
• Assumed Interest Rate:
• Compounded Annually
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Example 6
1.
2.
3.
4.
Simple Interest, P = \$10,000, APR = 6%, T = 8 Years
Compounded Annually, P = \$10,000, APR = 5%, T = 8 years
Compounded Daily, P = \$10,000, APR = 5%, T = 8 years
Accept \$13,000 8 years from now.
1. A = 10000+ 10000 x .06 x 8
2. A = 10000(1+(.05/1))^(1*8)
3. A = 10000(1+(.05/365))^(365*8)
4. A = NO INTEREST!
= \$14,800
= \$14,774.55
= \$14,917.84
= \$13,000
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Example 7
• Calculate the final amount in an account
receiving simple interest on an account of
\$5,000 at a rate of 5% APR after 5 years.
A = 5000 + 5000 x 0.05 x 5 = \$6,250
19
Example 8
• Calculate the final amount in an account
receiving compound interest on an account of
\$5,000 at a rate of 5% APR compounded
annually after 5 years.
A = 5000 x (1+(.05/1))^(1 x 5) = \$6,381.41
20
Example 9
1. Bank of Anthony:
Simple Interest, P = \$10,000, APR = 6%, T = 10 Years
2. Bank of Daisy:
Compounded Annually, P = \$10,000, APR = 5.5%, T = 10 years
3. Bank of Bree:
Compounded Semiannually, P = \$10,000, APR = 5%, T = 10 years
4. Bank of Jennifer:
Compounded Monthly, P = \$10,000, APR = 4.9%, T = 10 years
5. Bank of Luis:
Compounded Daily, P = \$10,000, APR = 4.8%, T = 10 years
21
Example 9
1. Bank of Anthony: = \$16,000
Simple Interest, P = \$10,000, APR = 6%, T = 10 Years
2. Bank of Daisy:
= \$17,081.44
Compounded Annually, P = \$10,000, APR = 5.5%, T = 10 years
3. Bank of Bree:
= \$16,386.16
Compounded Semiannually, P = \$10,000, APR = 5%, T = 10 years
4. Bank of Jennifer: = \$16,306.88
Compounded Monthly, P = \$10,000, APR = 4.9%, T = 10 years
5. Bank of Luis:
= \$16,160.23
Compounded Daily, P = \$10,000, APR = 4.8%, T = 10 years
22
Federal Deposit Insurance Corporation
• FDIC
• Insures low risk investments
– Checking
– Savings
– Certificates of Deposits
– Money Market Accounts
• Limit up to \$250,000 per bank where your
money is stored
– (Up from \$100,000 before Financial Meltdown)
23
CDs – Certificates of Deposit
• Your principal is “locked in” for a fixed period
of time (6 months, 1 year, 5 years, etc.)
• Typically offers higher interest rate when
compared with savings accounts
• Low Risk
• Some are variable rate
• Bankrate.com
24
CD’s Continued
• Locked in period expires = Reach Maturity
– You may take out or add to your principal during “Grace
Period”
– If you take out money before Grace Period, you are subject
to penalties (60 days interest)
– Penalties are just on interest collected. Never on principal
• To calculate interest lost,
1. Divide APR (as a decimal) by 12.
2. Multiply that decimal answer by principal
3. Multiply that answer by the number of months charged
by fee
4. You will lose that much in interest
• If fee >interest, you lose all interest accumulated
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27
APR or APY?
• APR does not take compounding into effect
• APY does take compounding into effect
• When performing calculations,
ALWAYS USE APR
• When comparing accounts,
ALWAYS USE APY
28
Example 10
• You decide to purchase a 3 year CD that has
an APR of 1.3%. It compounds daily. What will
be the amount in the CD once it reaches
maturity?
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Example 11
• You invest \$10,000 in a 5 year CD that has an
APR of 1.5%. It compounds monthly.
– What will be the amount in the CD once it reaches
maturity?
– You need money to buy Christmas presents, and
take out your money. There is a 2 month penalty.
About how much interest will you lose?
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Review of Interest
•
•
•
•
Always use APR in calculations
Simple Interest = P + P*R*T
Compound Interest = P(1+(r/n))^(n*t)
Calculate simple and daily compounded
interest on \$30,000 over 1 year.
31
Simple & Compound Interest Example
32
Money Market Accounts
• Like a savings account where you can write
checks off of
• Higher interest rates than savings/checking
accounts
• Catches:
– Minimum balance
• \$500 and up to \$50,000+ (jumbo)
– Less than 5 withdrawals a month
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Money Market Accounts
• Offered by banks and credit unions
• Insured by
– FDIC (Banks)
– NCUA – National Credit Union Association
• Invests in Treasury Bills, deposits, CDs, federal
funds, short term mortgages, and asset backed
securities
• Provides liquidity funding for global financial
system
• www.bankrate.com
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Lesson 5 End
• Review
• Quiz
36
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