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Managing your Personal Finances Unit 5 Banking
Earning Simple vs. Compound Interest
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Do Now1. If I told you to take a penny and double it each day for 30 days would it be worth it to you?
2. Can you think why a person who starts saving at a young age normally out saves someone who starts saving later in life?
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Please rate your understanding(Before lesson)
On a scale of 1 to 5 please rate your overall understanding of the following concepts:
Savings rates Simple Interest Time value of money Compound Interest My overall rating is a ________.
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Do Now(Answers)
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Standard5.3 Students will understand the
difference between earning simple and compound interest and will be able to calculate long term gains from savings.
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Goals of the day:I can:• understand the differences between
earning simple and compound interest• calculate the earnings from simple and compound interest
• understand the Rule of 72 (and calculate how long it will take to double my money using the Rule)
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What is Interest?
Interest is the amount you earn when you save money with a
bank (in a savings account).
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Simple Interest Formula
Principal – an amount of money that is lent, borrowed, saved or invested.Rate – interest rate (expressed as a decimal 6% or .06)Time – time period (usually in years)
Simple Interest = Principal * Rate * Time
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Simple Interest Practice
Working Together–You saved $1,000 for 1 year at 4%.What is the amount of interest you can expect to receive at the end of 1 year? What will be your Total Principal and Interest earned?
To calculate Interest earned:$1,000.00 * .04 * 1 = $40.00
To calculate total amount due (Principal + Interest : Principal ($1,000.00) + Simple Interest ($40.00) =
Total ($1,040.00)
Simple Interest =Principal * Rate * Time
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Simple Interest Practice
Practice On your Own #1-You saved $25,000 for 25 years at 6%. What is the amount of interest you can expect to receive at the end of 1 year? What will be your Total Principal and Interest earned?Calculate Simple Interest earned: $_____________Show your work here:
Calculate total amount due (Principal and Interest): $________________________ Show your work here:
Simple Interest =Principal * Rate * Time
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Simple Interest Practice
Practice On your Own #2 ––You saved $10,000 for 50 years at 10%. What is the amount of interest you can expect to receive at the end of 1 year? What will be your Total Principal and Interest earned?Calculate Principal Interest earned: $_____________Show your work here:
Calculate total amount due (Principal and Interest): $________________________ Show your work here:
Simple Interest =Principal * Rate * Time
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Calculating Interest Handout
Please complete Part 1 of the Simple and Compound Interest Handout.
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Calculating Interest Handout
What is the relationship between interest rates and your overall return on your savings investment?
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Compound Interest Compound Interest is calculated on the initial
principal and also on the accumulated interest of previous periods of a deposit or loan.
Compound Interest can be thought of as “interest on interest” and will make a deposit or a loan grow at a faster rate than Simple Interest (which is interest calculated only on the principal amount.)
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Compound Interest (Cont.) The rate at which compound interest accrues depends on
the frequency of compounding; the higher the number of compounding periods, the greater the compound interest.
Compounding Factors: Annual - 1 Semi-annual - 2 Quarterly - 4 Monthly - 12 Daily - 365
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Frequency of Compounding
As frequency of compounding
Interest Income received at end of period
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Calculate Compound Interest
Formula: FV=PV(1+r/m)^m*t
FV- Future Value PV-Present Value r-rate m-compounding factor t- time
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Compounding FactorsAnnual- 1
Semi-annual- 2Quarterly- 4Monthly- 12Daily- 365
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Calculate Compound Interest
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#1 Together: Calculate Compound Interest on principal of $2,500.00 at 6% compounded annually for 10 years.
Step 1: Identify the components of the problem:PV _______r_________m________ t_______________
Formula: FV=PV(1+r/m)^m*t
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Calculate Compound Interest
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#1 Together: calculate Compound Interest on principal of $2,500.00 at 6% compounded annually for 10 years. PV = $2,500 r = 6% m = 1 t = 10 Step 2: Create the formula here:
2500(1+(.06/1))^1*10Step 3: Plug the numbers into your calculator and solve
$________________________.
Compound Interest Formula: FV=PV(1+r/m)^m*tSample calculator keys:
FV=PV(1+(r/m))^(m*t)
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Remember to Round Your Answers to Dollars!
Calculator Keys:2500(1+(.06/1))(1*10)
4,477.119241 is rounded to $4,477.12
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Calculate Compound Interest
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#2 Together: calculate Compound Interest on principal of $5,000.00 at 8% compounded annually for 10 years.Step 1. Identify the components of the problem: PV_______ r_______ m_______ t_______ Step 2: Create the formula here:
Step 3: Plug the numbers into your calculator and solve $________________________ (remember to round to $$’s)
Compound Interest Formula: FV=PV(1+r/m)^m*tSample calculator keys:
FV=PV(1+(r/m))^(m*t)
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Calculate Compound Interest
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#1 On Your Own: Calculate Compound Interest on principal of $8,000.00 at 7% compounded monthly for 25 years.Step 1. Identify the components of the problem PV_______ r_______ m_______ t_______ Step 2: Create the formula here:
Step 3: Plug the numbers into your calculator and solve $________________________ (remember to round to $$’s)
Compound Interest Formula: FV=PV(1+r/m)^m*tSample calculator keys:
FV=PV(1+(r/m))^(m*t)
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Calculate Compound Interest
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#2 On Your Own: calculate Compound Interest on principal of $8,000.00 at 7% compounded monthly for 25 years.Step 1. Identify the components of the problem PV_______ r_______ m_______ t_______Step 2: Create the formula here:
Step 3: Plug the numbers into your calculator and solve $________________________ (remember to round to $$’s)
Compound Interest Formula: FV=PV(1+r/m)^m*tSample calculator keys:
FV=PV(1+9r/m))^(m*t)
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Calculating Interest Handout
Please complete Part 2 of the Simple and Compound Interest Handout.
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Calculating Interest Handout
What did you discover about the around of interest you earned:1.With Simple Interest compared to Compound Interest?2.When you increased the frequency of compounding?3.When you increased the interest rate?
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Rule of 72
Quick way of finding out how long it will take to double your money!
Rule was first mentioned in anarithmetic book published in 1494.
Rule is: The number 72 divided by the interest rate The result is the number of years it will take to
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Rule of 72 (continued)
Working Together:
If you save $2,000 at a 8% interest rate, how many years will it take to grow into $4,000?
Rule of 72 formula:
72/Interest Rate (expressed as a number) 72/8= 9
It would take 9 years to double your money!
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Rule of 72 (continued)
Working On Your Own:
Calculate how many years will it take $1,500 to double if it grows at an interest rate of 6%?
$________________________Show your work here:
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Rule of 72 (Now you try!)
On Your Own:
Calculate the number of years it will take to double your money at Interest Rates of 12%, 9%, 4%, and 2%
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12% _____
9% _____
4% _____
2% _____
What is the relationship between the rate of interest and how long it will take you to double your money?
__________________________
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DO NOW: Laurel and Hardy Handout(Apply Compound Interest Formula)
See Handout:
Laurel and Hardy start an advertising business. They hope to do well and expect to retire someday. Laurel, who turned 25, is a saver. He puts $10,000 into his retirement account right away and intends to leave it there until he turns 60 (35 years) . Hardy, is more of a spender. He waits until he is 40 to put money away for his retirement. He realizes that he is way behind Laurel so he puts $20,000 into his retirement account and intends to keep it there until he is 60 (20 years).
Both gentlemen shopped around and found a bank that offered 8% interest compounded daily.
How much money do both of them have at age 60?
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Exit Ticket
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Please explain the picture below as it relates to Simple Interest vs. Compound Interest :
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Exit Ticket Answer…
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Please rate your understanding(After lesson)
On a scale of 1 to 5 please rate your overall understanding of the following concepts:
Savings rates Simple Interest Time value of money Compound Interest Now my overall rating is a ________.
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