Managing your Personal Finances Unit 5 Banking Earning Simple vs. Compound Interest 1.

Managing your Personal Finances Unit 5 Banking

Earning Simple vs. Compound Interest

1

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?

2

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 ________.

3

Do Now(Answers)

1.

2.

4

Standard5.3 Students will understand the

difference between earning simple and compound interest and will be able to calculate long term gains from savings.

5

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)

What is Interest?

Interest is the amount you earn when you save money with a

bank (in a savings account).

7

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

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


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:



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:


Calculating Interest Handout

Please complete Part 1 of the Simple and Compound Interest Handout.


What is the relationship between interest rates and your overall return on your savings investment?

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.)

14

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

15

Frequency of Compounding

As frequency of compounding

Interest Income received at end of period

16

Calculate Compound Interest

Formula: FV=PV(1+r/m)^m*t

FV- Future Value PV-Present Value r-rate m-compounding factor t- time

17

Compounding FactorsAnnual- 1

Semi-annual- 2Quarterly- 4Monthly- 12Daily- 365


18

#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


19

#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)

Remember to Round Your Answers to Dollars!

Calculator Keys:2500(1+(.06/1))(1*10)

4,477.119241 is rounded to $4,477.12


21

#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)




22

#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:





23

#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:



FV=PV(1+9r/m))^(m*t)


Please complete Part 2 of the Simple and Compound 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?

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

double your money26

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!

27

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:

28

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%

29

12% _____

9% _____

4% _____

2% _____

What is the relationship between the rate of interest and how long it will take you to double your money?

__________________________

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?

30

Exit Ticket

31

Please explain the picture below as it relates to Simple Interest vs. Compound Interest :

Exit Ticket Answer…

32

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 ________.

33

Managing your Personal Finances Unit 5 Banking Earning Simple vs. Compound Interest 1.

Documents

Transcript of Managing your Personal Finances Unit 5 Banking Earning Simple vs. Compound Interest 1.