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**Value of money saved in accounts increases!**

Time Value of Money Value of money saved in accounts increases! Time value of money- money paid in future is not equal to money paid today

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**Factors affecting the Time Value of Money**

Save for as long as possible! Amount of Money Save as much as possible, as often as possible! Interest Rate Save at the highest interest rate possible!

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**Time Value of Money Magic!**

Year 20 Interest Earned: $111.07 Amount Savings is Worth: $386.97 Year 15 Interest Earned: $79.19 Amount Savings is Worth: $275.90 Initial Savings: $ at 7% interest Year 1 Interest Earned: $7.00 Amount Savings is Worth: Year 10 Interest Earned: $56.46 Amount Savings is Worth: $196.72 Year 5 Interest Earned: $33.26 Amount Savings is Worth: $140.26 Year 50 Interest Earned: $845.46 Amount Savings is Worth: $

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**How do you choose to save money over spend money?**

Pay Yourself First! A Strategy Set aside money for saving before spending any money Save then spend! Creates a habit Saving is not what is left at end of month Why?

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**To successfully practice “pay yourself first”…**

Set goals! Goal- End result of something a person intends to accomplish Financial Goal- Specific objectives to be accomplished through financial planning

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**What is a trade-off to saving money for the future?**

What are you willing to give up to obtain the item you want to purchase? This is a trade-off! Trade-off - giving up one thing for another Every decision you make involves a trade-off! What is a trade-off to saving money for the future? Being more financially secure in the future by saving money is a trade-off to spending money in the present

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**In order to choose saving money over spending money…**

“Pay Yourself First” To successfully practice this strategy… Set financial goals Examine trade-offs Examine current spending

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**Simple Interest vs. Compound Interest**

Interest earned on the principal investment Earning interest on interest Principal is the original amount of money invested or saved

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**Simple Interest Equation: Step 1**

(Principal) P (Interest Rate) r (Time Period) t (Interest Earned) I 1,000 .07 5 350.00 $1,000 invested at 7% interest rate for 5 years

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**Simple Interest Equation: Step 2**

(Principal) P (Interest Earned) I (Amount Investment is Worth) A $1,000 invested at 7% interest rate for 5 years 1,000 350 $1,350.00

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**Compound Interest Equations**

There are two methods for calculating compound interest Single sum of money Money invested only once at the beginning of an investment Equal number of investments spread over time Equal amounts of money are invested multiple times (once a month, once a year, etc.)

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**Compound Interest Equation – Single Sum**

P (1 + r)n = A Amount Investment is Worth Principal (1 + Interest Rate)Time Periods = $1,000 invested at 7% interest rate compounded yearly for 5 years 1,000 (1+ .07)5 = $

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**Compound Interest Equation - Multiple Investments in Equal Amounts**

PMT x (1+r)n-1 = A r Payment x (1+Interest Rate)Time Period-1 = Amount Investment is Worth Interest Rate $1,000 invested every year at 7% annual interest rate for 5 years 1,000 x (1+.07)5-1 = $5,757.00 .07

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**Time Value of Money Math Practice #1**

Sara deposited $ into a savings account one year ago. She has been earning 1.2% in annual simple interest. Complete the following calculations to determine how much Sara’s money is now worth. Step One: 600.00 .012 1 7.20 Step Two: 600.00 7.20 607.20

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**Time Value of Money Math Practice #1**

How much is Sara’s investment worth after one year? $607.20

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**Time Value of Money Math Practice #2**

Tim’s grandparents have given him $ to invest while he is in college to begin his retirement fund. He will earn 2.3% interest, compounded annually. What will his investment be worth at the end of four years? What is the equation? $1,500 ( )4

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**Time Value of Money Math Practice #2**

Step One: 1 .023 1.023 Step Two: 4 1.023 1.095 Step Three: 1.095 1500

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**Time Value of Money Math Practice #2**

What will Tim’s investment be worth at the end of four years? $

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**Time Value of Money Math Practice #3**

Nicole put $ into an account that pays 2% interest and compounds annually. She invests $ every year for five years. What will her investment be worth after five years? What is the equation? $2,000 x (1+.02)5-1 .02

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**Time Value of Money Math Practice #3**

Step One: 1 .02 1.02 Step Two: 5 1.02 1.104 Step Three: 1.104 1 .104

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**Time Value of Money Math Practice #3**

Step Four: .104 .02 5.2 Step Five: 5.2 2000 10,400.00 What will Nicole’s investment be worth at the end of five years? $10,400.00

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Chapter 5 Mathematics of Finance.

Chapter 5 Mathematics of Finance.

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