HACE 3200 1nd Edition Lecture 6Outline of Last Lecture I. Practice Problems for RatiosOutline of Current Lecture I. Time Value of MoneyII. Interest and Compound InterestIII. Future Value EquationIV. Present Value EquationCurrent Lecture- 1/22/14- Understanding The Time Value of Moneyo A dollar received today is worth more than a dollar received in the futureo The sooner your money can earn interest, the faster the interest can earn interest.- Interest and Compound Interesto Interest(i)- is the return you receive for investing your moneyo 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 $100o Reminders.. 3%= .03 in decimal formo 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 $100o Deposit( $X) + Deposit ($X) times interest rate (i) = new account balanceo 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. balanceo = $X (1 + i)= new account balanceo =$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 ORo X( 1 = i) N X= $$ deposit I = % interest rate Where n = number of periods you are compounding- Practice Problemso 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 Calculatoro 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 goo Key in 10 then hit the PV keyo 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 keyo 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 72o Estimates how many years an investment will take to double in valueo 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 timeo 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 Equationo 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 moneyo This equation is used to determine the value of an investment at some point in the future- Practice Problemso 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 Calculatorso PV= 1000, N= 15, I/Y= 11; CPT FV= $4,784.58o PV=1500, N=20, I/Y= 8; CPT FV= $6,991.44- Determining the Present Value of your moneyo 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 Equationo 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 Problemso 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: Inflationo 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!- Summaryo FV= PV(1+ i)n What your money will grow to beo PV= FV( 1/(1+i)n What your future money is worth todayo Inflation adjusted interest rate( i*) Substituting i* for I when controlling for