CIVL 403 - Formulae and Data Sheets Compound Interest F= Px (1+ i)^N ie = [1+ (r/m)]^m - 1 ie = exp(r) - 1 for continuous compounding Compound Interest Factors (contd.) Arithmetic series (P/G, i, N) = [(1+i)^N -iN- 1] / [i^2x (1 + i)^N] (A/G, i, N) = (1/i) - {N/ [(1+i)^N - 1]} Geometric series (P/A, g, i, N) = (P/A, io, N) / (1+g) with io = (1 +i)/(1 + g) - 1 Note: when io = 0, P = AN / (1+g) Compound Interest Factors (F/P,i,N)=(1+i)^N (P/F,i, N) = 1/[(1+i)^N] (A/F, i, N) = i / [(1+i)^N - 1)] (F/A, i, N) = [(1+i)^N - 1] / i (A/P, i, N) = i(1+i)^N / [(1+i)^N - 1] (P/A, i, N) = [(1+i)^N - 1] / [i(1+i)^N] Cash flow diagrams for common cash transactions 1 2 3 4 5 1 2 3 4 5 (a) single disbursement and receipt (b) annuity 1 2 3 4 5 1 2 3 4 5 (c) arithmetic gradient series (d) geometric gradient series Infinite life (P/A, i, N -> 00) = 1/i P = A/i Evaluation of Projects & Replacement Decisions Payback period, constant annuity: P/A Discounted payback period, constant annuity: - In[1 - i(P/A)] / In(1+i) Net Present Value = > Rt/(1+i)t 00000000 = 00 * (44) + 00 * (44) + 00 * (00)
Compound Interest Factor Tables [Discrete Compounding, Discrete Cash Flows] SINGLE PAYMENT ANNUITY i = 5% N (F/P,i,N) 1 1.050 2 1.103 3 1.158 0.864 0.317 3.153 4 1.216 0.823 0.232 4.310 5 1.276 6 1.340 0.746 0.147 6.802 0.197 7 1.407 0.711 0.123 8.142 0.173 8 1.477 0.677 0.105 9.549 9 1.551 0.645 0.091 11.027 10 11 1.629 1.710 12 1.796 0.557 0.063 13 1.886 0.530 0.056 14 1.980 0.505 0.051 19.599 0.101 0.096 15 2.079 0.481 16 2.183 0.458 17 2.292 18 2.407 19 2.527 20 2.653 0.377 i = 10% N (F/P,i,N) (P/F,i,N) 1 1.100 0.909 2 1.210 0.826 0.476 2.100 3 1.331 0.751 0.302 3.310 4 1.464 0.683 5 1.611 0.621 0.564 6 1.772 7 1.949 0.513 0.105 9.487 8 2.144 0.467 0.087 11.436 9 2.358 0.424 10 2.594 0.386 2.853 0.350 11 12 3.138 0.319 0.047 13 3.452 0.290 0.041 14 3.797 15 4.177 16 4.595 17 5.054 18 5.560 19 6.116 20 6.727 i = 15% N (F/P,i,N) (P/F,i,N) (A/F,i,N) 1 1.150 0.870 1.000 1.000 2 1.323 0.756 3 1.521 0.658 4 1.749 0.572 5 2.011 0.497 6 2.313 0.432 7 2.660 8 3.059 0.327 0.073 13.727 0.223 9 3.518 0.284 0.060 16.786 0.210 10 4.046 11 4.652 0.215 12 5.350 0.187 0.034 13 6.153 0.163 0.029 14 7.076 15 8.137 16 9.358 17 10.761 0.093 0.015 18 12.375 0.081 0.013 19 14.232 20 16.367 (P/F,i,N) 0.952 1.000 0.907 0.488 2.050 0.784 0.181 5.526 0.231 0.614 0.585 0.070 0.436 0.039 0.416 0.396 0.263 0.239 0.218 0.198 0.025 0.180 0.022 0.164 0.020 0.149 0.376 0.090 11.067 0.247 0.141 0.123 0.107 0.070 0.011 0.061 0.010 (A/F,i,N) 0.080 12.578 14.207 0.046 0.042 0.036