1. Show your work of how to derive Equation B from Equation A by hand. 2. Do the same from A to C. 3. Do the same from A to D. 4. Do the same from A to E. 5. Do the same from B to F. 6. Do the same from G to H. Time Value of Money Table A Annual Compounding TVM Formula B m Compounded Per Year Detail 1 Compounding EV = PV 1245 A A FV = PV (1+1/mym 2 FT Discounting FV PV = (1+1) PV = (l+ilm) Ne 3 FV FVM PV FV of a lump sum PV of a lump sum The interest rate required for a PV to grow to a FV The length of time required for a PV to grow to a FV FV of annuity PP IC FV In PV N = In(1+i) N D FV In PV min(1+/m) 5 FV=C(+)"=1 FV =cl+i/w)-1 FV=C(C1/C 6 PV of annuity pv=c!-(1+) 1-(1+/) PIC // PE (+)' (1 i (1) 7 G PV =- PI Infinite annuity (1+/m-1 8 C PV = 9 PV of perpetuity PV of growing perpetuity Net Present Value (NPV) Internal Rate of Return (IRR) EAR VS. APR NPV - C (1+1) Infinite but growing cash flows NPV = PV(Benefits) minus PV(Costs) IRR is the rate that forces a zero NPV. Periodic rate = APR/m 10 NPVA 1 (1 IRR) 11 EAR = (1 + APR / m) - 1 APR = m((1 + EAR)-1] H G G