HACE 3200 1nd Edition Lecture 6 Outline of Last Lecture I Practice Problems for Ratios Outline of Current Lecture I Time Value of Money II Interest and Compound Interest III Future Value Equation IV Present Value Equation Current Lecture 1 22 14 Understanding The Time Value of Money o A dollar received today is worth more than a dollar received in the future o The sooner your money can earn interest the faster the interest can earn interest Interest and Compound Interest o Interest i is the return you receive for investing your money o Compound interest is the interest that your investment earns on the interest that your investment previously earned o Inflation r is when rising prices reduce the purchase power of money The Effect of 3 interest on a One Time Deposit of 100 o Reminders 3 03 in decimal form o On your calculator hit the 3 key and then hit the key 4th row from the top left hand side The Effect of 3 interest on a One Time Deposit of 100 o Deposit X Deposit X times interest rate i new account balance o For example 100 X 3 100 03 X 03 103 Or in one easy step These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute o Your deposit X multiplied by 1 the interest rate in decimal form new acct balance o X 1 i new account balance o 100 1 03 103 X X i X 1 i The Effect of Compounding Interest over time long form o X 1 i 3 X4 OR o X 1 i N X deposit I interest rate Where n number of periods you are compounding Practice Problems o How much will you have in savings if you deposit 10 and leave it in an account earning 5 interest compounded annually for 10 years o How much will you have in savings if you deposit 100 in an account earning 12 compounded annually for 20 years Financial Calculator o PV 10 dollars o I Y 5 Percent o N 10 Years Periods Compute FV Future Value o PV 100 dollars o I Y 12 percent o N 20 years Periods Compute FV Future Value o With your financial calculator you enter the number and then tell it where to go o Key in 10 then hit the PV key o Key in 5 then hit the i y key don t change to decimal it does it for you o Key in 10 hit the N key o Hit CPT FV key to show answer 16 28 964 63 Your answer will show up as a negative number That is expected because the 10 was an outflow of cash from one s current consumption to one s retirement account If you don t want your answer to show up as negative then you have to make the PV negative The Rule of 72 o Estimates how many years an investment will take to double in value o Number of years to double 72 annual compound growth rate o Example 72 8 9 therefore it will take 9 years for an investment to double in value if it earns 8 annually Determining the Future Value of your Money over time o Future value FV is the value to which your money will grow at a specific compounding Interest rate i o Future value is hypothetically moving your money forward n numbers of periods days months years Future Value Equation o FV PV 1 i n FV the future value of the investment at the end of n numbers of periods I the annual percentage interest rate APR PV the present value in today s dollars of a sum of money o This equation is used to determine the value of an investment at some point in the future Practice Problems o What is the future value FV of 1 000 at the end of 15 years if it is invested in an account bearing 11 annually APR o What is the future value FV of 1 500 after 20 years if it is invested in an account earning 8 annually APR Financial Calculators o PV 1000 N 15 I Y 11 CPT FV 4 784 58 o PV 1500 N 20 I Y 8 CPT FV 6 991 44 Determining the Present Value of your money o Present Value PV is hypothetically moving dollars from the future back into the present at a specific interest rate i for a specific number of periods n o Inverse compounding Present Value Equation o PV FV 1 1 i n PV the present value in todays dollars of a sum of money FV the future value of the investment at the end of n years I annual interest rate N number of periods This equation is used to determine today s value of some future sum of money Practice Problems o Josh is due to receive his inheritance 100 000 in 5 years It is in an account earning 10 annually Josh wants his money now If josh withdraws his money today how much will he receive FV 100 000 N 5 I Y 10 CPT PV 62 092 Interest s Enemy Inflation o An economic condition in which rising prices reduce the purchasing power of money Inflation adjusted interest rate i o Substitute i for I during PV and FV formulas I the interest rate R inflation rate In your financial calculator the I in I Y is now replaced with I the inflation adjusted interest rate You MUST calculate the I first Summary o FV PV 1 i n What your money will grow to be o PV FV 1 1 i n What your future money is worth today o Inflation adjusted interest rate i Substituting i for I when controlling for inflation