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SUMMARY OF FORMULA (Discrete Compounding Interest Factors and Symbols) To Given: Factor by which to Factor Name Factor Functional find: multiply Symbol For Single Cash Flows F P (1+i)" Single Payment (F/P, 1%, n) Compound Amount P F (1+i)-" Single Payment (P/F, 1%, n) Present Worth For Uniform Series F A (1+i)" -1 Uniform Series (F/ A, 1%, n) Compound Amount i P A (1+i)" -1 Uniform Series (P/A, 1%, n) Present Worth i(1+i)" A F i Sinking Fund (A/F, 1%, n) (1 +i)" -1 A P i(1 + i)" Capital Recovery (A/P, 1%, n) (1+i)" -1 The functional symbols and formulas used in dealing with a uniform arithmetic gradient are: For finding the present equivalent, P P = PA + PG (for increasing gradient) P = PA - PG (for decreasing gradient) Where: Po = G(P/G, 1%, n) (P/G, 1%, n) = (1+i)" -1 n i(1+i)" (1+i)"II. Solve the following problems. Show your complete solution {including formula: I factor. factor functional symbol f notation} and cash flow. {15 pointsl 1. A government employee is preparing for his retirement by making contributions to a savings program. Assume that PhF LBW is set aside yearly and invested in an account with 15% interest per year com pounded continuously. How much would he receive at the end of 3D years? 2. \"four department head gave you a summary of projected annual cost and revenues for your new project. He asked you to calculate the ERR for this investment opportunity. The company's MARE is l. What would be your recommendation to him? Also, use the conventional benefit-post ratio method to justify your recommendation. - -PhP45u.unn -PhP42.sua + W 92.800 - mp 385ml: . .ph. mun 3. From problem #2, your department head asked you also to know how long it would take to recover the capital using the modied payback period method. For finding the future equivalent, F F = FA + FG (for increasing gradient) F = FA - FG (for decreasing gradient) Where: Fo = G(F/G, 1%, n) (1+i)" -1 (F/G, 1%, n) = -n For finding the uniform equivalent, A A = A + AG (for increasing gradient) A = A - Ac (for decreasing gradient) Where: AG = G(A/G, 1%, n) (A/G, 1%, n) = i (1+i)" -1when i # f we can simplify the above equation by defining a "convenience rate," i 1+i ier 1+ f Thus, we can write the equation as: A 1+i P = 1+f 1= 1+ ) - * - * P = 1+ f = [ (Itis ) ( PIA, ia % , n ) = [ (1+ i ) P = 4 (P/ A,i, %, n) 1 + f When i= f and i =0 P =- A (P/ A, 0%, n) = nA 1+ f 1+ f Then, A= P( A/ P, 1%, n) SUMMARY OF FORMULA (Continuous Compounding and Discrete Cash Flows: Interest Factors and Symbols) To Given: Factor by which to Factor Name Factor Functional find: multiply Symbol For Single Cash Flows F P Continuous (F/P, ro, n) Compounding compound amount (single cash flow) P F e Continuous (P/F, Po, n) Compounding present equivalent (single cash flow)find: multiply Symbol For Single Cash Flows F P Continuous (F/P, ro, n) Compounding compound amount (single cash flow) P F e Continuous (P/F, ro, n) Compounding present equivalent (single cash flow) To Given: Factor by which Factor Name Factor Functional find: to multiply Symbol For Uniform Series F A Continuous (F/ A, ro, n) Compounding compound amount (uniform series) P A 2" -1 Continuous (P/ A, r%, n) compounding present e' -1) equivalent (uniform series) A F Continuous (A/F, r%, n) compounding sinking fund A P (e Continuous (A/P, r%, n) Compounding Capital e"-1 Recovery