Time Value of Money Family Economics & Financial Education

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 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

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 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 Year2 Years $1,100.00$1, $1,000 Invested at 10% Simple Interest Rate 1 Year2 Years $1,100.00$1,200.00

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Compounding Interest  Compounding interest -- Earning interest on interest  “Make your money work for you” $1,000 Invested Compounded Annually at 10% Interest Rate 1 Year2 Years $1,104.71$1,220.39

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Three Factors Affecting the Time Value Calculations  Time  Amount invested  Interest rate

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Time  The earlier an individual invests, the more time their investment has to compound interest and increase in value

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona A Little Goes a Long Way  Sally Saver puts away $3,000 per year in her IRA age 21, 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

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Amount Invested  small amount a month is better than nothing Ex. At 8% interest, invested at age 17, one dollar per day will become $17, by age 65  Larger amount invested = greater return  Always pay yourself first Savings should be a fixed expense

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona The Costs Add Up ItemAverage Yearly ExpenseFuture Value Daily cup of coffee at $2.50$912.50$38, Eating lunch out 5 days per week at a cost of $5-$10 each time $1, $2,600.00$55, $110, Daily can of soda or chips at $1.00 each or both a can of pop and chips $2.00 $ $ $15, $30, Daily candy bar at $1.00$365.00$15, Investing at age 18 at 8% interest until age 65.

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Interest Rate  The percentage rate paid on the money invested or saved Higher interest=more money earned $1,000 Invested Compounded Monthly Interest Rate1 Year5 Years10 Years 4%$1,040.74$1,221.00$1, %$1,061.68$1,348.85$1,819.40

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Interest Rates  Fixed interest rate -The rate will not change for the lifetime of the investment Rate guarantees a specific return = moderate risk  Adjustable interest rate- rate is raised or lowered at periodic intervals according to the prevailing interest rates in the market Rate can go up or down = more risk

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Risk  the uncertainty of the outcome of any given situation A higher interest rate generally has a greater risk

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Time Value of Money Calculations  Present value PV=(FV)(1+i) -N  Future value FV=(PV)(I+i) N I= Interest  Financial calculators may be used to complete these calculations.

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Review  Compounding interest earns interest on interest  Increased time=more interest earned  Higher principal=more interest earned  Higher interest rate=more interest earned

The Rule of 72 The most important and simple rule to financial success.

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Rule of 72 72=Years to double Interest Rate  The time it will take an investment (or debt) to double in value at a given interest rate using compounding interest.

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 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

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona What the “Rule of 72” can determine  How many years it will take an investment/debt to double at a given interest rate using compounding interest.  The interest rate an investment/debt must earn to double within a specific time period.

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 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? Do not change the percentage to a decimal. Use the exact number shown

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Jessica’s Credit Card Debt  $2,200 balance on credit card  18% interest rate 72=4 years to double debt 18% 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?

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Rhonda’s Treasury Note 72= 9.6 years 7.5%to double investment AgeInvestment 22$2, $5, $10, $20, $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?

G1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 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.