. 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. Take some papers out with pencil and start writing down your work A Annual Compounding TVM Formula B m Compounded Per Year Detail Compounding 1 FV = PV (1+i/m) 2 FV Discounting IB PV = (1+i/m) N 3 FVM im 1 Pr FV of a lump FV = PV (1+1) sum PV of a lump FV PV = sum (1+1) The interest FVN rate required -1 PV for a PV to grow IC to a FV The length of FV In time required PV N = for a PV to grow In(1+i) to a FV FV of annuity (1+1)-1 FV in PV mIn(1 + 7/m) N = D 5 FV FV=c(l+1/m)** -7 im M FV=C(1+1)C(1+/)+ ... + C (1+1) C c PI = + (1+1)! (140 (1+1) 6 PV of annuity PV = 1-(1+/m) 1m PV =C1-(1+1) 1 7 e PV =- PV = V = 8 PV N 9 PV of perpetuity PV of growing perpetuity Net Present Value (NPV) Internal Rate of Return (IRR) EAR VS. APR NPV = - C Infinite annuity (1+1/m)"- Infinite but growing cash flows NPV = PV(Benefits) minus PV(Costs) IRR is the rate that forces a zero NPV. APR = [(1 + EAR)/m - 11 Periodic rate = APR/m (1+1) 10 NPWRR 0 C (L+ IRR) 11 EAR = (1 + APR / m) - 1 G G