HACE 3200 1nd Edition Lecture 8 Outline of Last Lecture I Practice Problems for Present Value and Future Value Outline of Current Lecture I Solving for Future Value II Annuity III Amortized Loans Practice Problems Chapter 3 Time Value Money Quick review a single deposit 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 1 i 1 r 1 100 Substituting i when controlling for inflation Annuities multiple payments o 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 Annuities o Definition depositing an equal sum of money at the end of each time period for a certain number of periods allowing the money to grow o 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 Equation o 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 Problems o 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 10 o 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 25 o 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 Equation o 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 unknown o CPT PV Present Value of an Annuity An example Alimony o What is the present value of 25 annual payments of 50 000 offered to a soonto 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 settlement o 25 annual payments of 50 000 invested at 5 results in 2 386 354 94 o A difference of 1 681 354 94 Amortized Loans o Definition loans that are repaid in equal periodic installments o 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 Installments o 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 59 o 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 payments o PV 6000 o 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 investment o Rule of 72 estimates how long your investment will take to double at a given rate of return o Present Value today s value of an investment received in the future o Annuity a periodic series of equal payments for a specific length of time o Future Value of Annuity the value in the future of a current stream of investments o Present Value of Annuity today s value of a stream of investments received in the future o Amortized loans loans paid in equal periodic installments for a specific length of time