Family Economics & Financial Education Time Value of Money Family Economics & Financial Education

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

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 Year 2 Years $1,100.00 $1,200.00 $1,000 Invested at 10% Simple Interest Rate 1 Year 2 Years $1,100.00 $1,200.00

$1,000 Invested Compounded Annually at 10% Interest Rate Compounding Interest Compounding interest -- Earning interest on interest “Make your money work for you” $1,000 Invested Compounded Annually at 10% Interest Rate 1 Year 2 Years $1,104.71 $1,220.39

Three Factors Affecting the Time Value Calculations Amount invested Interest rate

Time The earlier an individual invests, the more time their investment has to compound interest and increase in value

A Little Goes a Long Way Sally Saver puts away $3,000 per year in her IRA account @ 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

Amount Invested small amount a month is better than nothing Ex. At 8% interest, invested at age 17, one dollar per day will become $17,865.52 by age 65 Larger amount invested = greater return Always pay yourself first Savings should be a fixed expense

The Costs Add Up Investing at age 18 at 8% interest until age 65. Item Average Yearly Expense Future Value Daily cup of coffee at $2.50 $912.50 $38,704.46 Eating lunch out 5 days per week at a cost of $5-$10 each time $1,300.00-$2,600.00 $55,140.60 $110,281.21 Daily can of soda or chips at $1.00 each or both a can of pop and chips $2.00 $365.00 $730.00 $15,481.78 $30,963.57 Daily candy bar at $1.00

Interest Rate The percentage rate paid on the money invested or saved Higher interest=more money earned $1,000 Invested Compounded Monthly Interest Rate 1 Year 5 Years 10 Years 4% $1,040.74 $1,221.00 $1,490.83 6% $1,061.68 $1,348.85 $1,819.40

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

Risk the uncertainty of the outcome of any given situation A higher interest rate generally has a greater risk

Time Value of Money Calculations

Simple interest examples 1. Sarah deposits $4,000 at a bank at an interest rate of 4.5% per year. How much interest will she earn at the end of 3 years? 2. Wanda borrowed $3,000 from a bank at an interest rate of 12% per year for a 2-year period. How much interest does she have to pay the bank at the end of 2 years? 3. Raymond bought a car for $40,000. He took a $20,000 loan from a bank at an interest rate of 15% per year for a 3-year period. What is the total amount (interest and loan) that he would have to pay the bank at the end of 3 years?

Compounding Interest Formula

Compounding Interest examples 1. If you have a bank account whose principal = $1,000, and your bank compounds the interest twice a year at an interest rate of 5%, how much money do you have in your account at eh year’s end? 2. If you start a bank account with $10,000 and your bank compounds the interest quarterly at an interest rate of 8%, how much money do you have at the year’s end? (assume that you do not add or withdraw any money from the account)

Compounding interests examples 3. The first credit card that you got charges 12.49% interest to its customers and compounds that interest monthly. Within one day of getting your first credit card, you max out the credit limit by spending $1,200. If you do not buy anything else on the card and you do not make any payment, how much money would you owe the company after 6 months? 4. You win the lottery and get $1,000,000. You decide that you want to invest all of the money in a savings account. However, your bank has two different plans. In 5 years from now, which plan will provide you with more money? First Plan: The bank gives you 6% interest rate and compounds the interest each month. Second Plan: The bank gives you a 12% interest rate and compounds the interest every 2 months

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.

Rule of 72 The time it will take an investment (or debt) to double in value at a given interest rate using compounding interest. 72 = Years to double Interest Rate

“It is the greatest mathematical discovery of all time.” Albert Einstein Credited for discovering the mathematical equation for compounding interest, thus the “Rule of 72” T=P(I+I/N)YN P = original principal amount I = annual interest rate (in decimal form) N = number of compounding periods per year Y = number of years T = total of principal and interest to date (after n compounding periods) “It is the greatest mathematical discovery of all time.”

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.

Doug’s Certificate of Deposit 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? Invested $2,500 Interest Rate is 6.5% 72 = 11 years to double investment 6.5% Do not change the percentage to a decimal. Use the exact number shown

Jessica’s Credit Card Debt 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? $2,200 balance on credit card 18% interest rate This equation assumes that no additional payments or late fees were charged Generally minimum payments on credit cards are 2% of the account balance each month 72 = 4 years to double debt 18%

Rhonda’s Treasury Note 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? Age Investment 22 $2,500 31.6 $5,000 41.2 $10,000 50.8 $20,000 60.4 $40,000 70 $80,000 72 = 9.6 years 7.5% to double investment

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.