HACE 3200 1nd Edition Lecture 8Outline of Last Lecture I. Practice Problems for Present Value and Future ValueOutline of Current Lecture I. Solving for Future ValueII. AnnuityIII. Amortized Loans- Practice Problems Chapter 3: Time Value Money- Quick review: a single deposito 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: (1+i)/(1+ r)-1 *100 Substituting i* when controlling for inflation- Annuities : multiple paymentso Definition- a series of Equal payments coming at the end of a certain time period for a specified number of time periods (n).o Examples: Mortgages, life insurance benefits, lottery payments, retirement payments- Compound Annuitieso Definition- depositing an equal sum of money at the end of each time period for a certain number of periods allowing the money to growo Example: having $50 taken out of each paycheck and put it in a Christmas account earning 9% Annual Percentage Rate- Future Value of an Annuity (FVA) Equationo This equation is used to determine the future value of a stream of deposits/ payments (PMT) invested at a specific interest rate( i) for a specific number of periods(n)o For example: the value of your 401 K contributions- Calculating the Future Value (FVA) of an Annuity:o Assuming a $2000 annual contribution with a 9% rate of return, how much will an IRA be worth in 30 years?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. PMT= 2000 I/Y= 9 N=30 CPT FV= $272,615- Solving for Future Value o Each Month, Anna deposits her paycheck ($5000) in an account offering a Monthly interest rate of 6%. How much will Anna have in her account at the end of 1 year? PMT= 5000 I/Y= 6 N=12 ( because it is deposited monthly, you have to multiply by 12) CPT FV= $84,349.70 at the end of one year- Practice Problemso If jenny deposits $1,200 each year into a savings account earning an Annual Rate of return of 2% for 15 years, how much will she have at the end of the 15 years? PMT= $1,200 I/Y= 2 N= 15 CPT FV= $20,752.10o How much will she have if she deposits $1,200 each Month? How much will she have if she earns interest monthly? If the payments is a monthly payment; then the compounding rate of return has to be a monthly rate of return Example: A 15% ANNUAL rate of return is equal to a monthly rate of return of 1.25% 15/12= 1.25o Monthly  PMT=$1,200 I/Y= .1667(2/12) N=180(15*12) CPT FV= $251,655.66- Present Value( moves backwards) & Future Value( moves forward)o In real life: winning the lottery( present value) or saving for retirement( future value)- Present Value of an Annuity( PVA) Equationo This equation is used to determine the present value of a future stream of payments, such as your pension fund or insurance benefits- Solving for Present Value of an Annuity( Multiple)o The present value is the unknowno CPT PV- Present Value of an Annuity: An example: Alimonyo What is the present value of 25 annual payments of $50,000 offered to a soon-to-be-ex wife, assuming a 5% annual discount rate?(PVA is the only unknown PMT= 50,000 N=25 I/Y=5 CPT PV= $704, 697. 228- Future Value Annuity of that divorce settlemento 25 annual payments of $50,000 invested at 5% results in $2,386,354.94o A difference of: $1,681,354.94- Amortized Loanso Definition- loans that are repaid in equal periodic installmentso With an amortized loan the interest payments declines as your outstanding principal declines; therefore, with each payment you will be having an increasing amount towards the principal of the loan.o Examples: car loans, or home mortgages- Buying a car with 4 easy Annual Installmentso What are the annual payments to repay $6,000 at 15% interest? ( the payments is the unknown) PV=6000 I/Y=15 N=4 CPT PMT= 2,101,59o Make double sure your time frames are consistent  If the payments is a monthly payments; then the compounding rate of return has to be a monthly rate of return Example: a 15% ANNUAL rate of return is equal to a monthly rate of return of 1.25% 15/12= 1.25- Buying the Same car with monthly paymentso PV=6000o I/Y=1.25(15/12)o N=48( 4*12)o CPT PMT= $166.98- Review:o Future Value- the value, in the future, of a current investmento Rule of 72- estimates how long your investment will take to double at a given rate of returno Present Value- today’s value of an investment received in the futureo Annuity- a periodic series of equal payments for a specific length of timeo Future Value of Annuity- the value, in the future, of a current stream of investmentso Present Value of Annuity- today’s value of a stream of investments received in the futureo Amortized loans- loans paid in equal periodic installments for a specific length of