Question 4) Find the value of cash flow X that will make the two cash flows equivalent. Interest is 10% compounded annually.Time on the diagram is given in years. 3 100 120 2 1 140 160 F = P(1 + i)" A=G i (1+i)" - 1 4% n 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 F = A (1+i)" - 1 n P=A (1+i)" -1 i i(1+i)" TABLE 9 Discrete Cash Flow: Compound Interest Factors 4% Single Payments Uniform Series Payments Arithmetic Gradients Compound Present Sinking Compound Capital Present Gradient Gradient Amount Worth Fund Amount Recovery Worth Present Worth Uniform Series F/P P/F AF F/A A/P P/A P/G A/G 1.0400 0.9615 1.00000 1.0000 1.04000 0.9615 1.0816 0.9246 0.49020 2.0400 0.53020 1.8861 0.9246 0.4902 1.1249 0.8890 0.32035 3.1216 0.36035 2.7751 2.7025 0.9739 1.1699 0.8548 0.23549 4.2465 0.27549 3.6299 5.2670 1.4510 1.2167 0.8219 0.18463 5.4163 0.22463 4.4518 8.5547 1.9216 1.2653 0.7903 0.15076 6.6330 0.19076 5.2421 12.5062 2.3857 1.3159 0.7599 0.12661 7.8983 0.16661 6.0021 17.0657 2.8433 1.3686 0.7307 0.10853 9.2142 0.14853 6.7327 22.1806 3.2944 1.4233 0.7026 0.09449 10.5828 0.13449 7.4353 27.8013 3.7391 1.4802 0.6756 0.08329 12.0061 0.12329 8.1109 33.8814 4.1773 1.5395 0.6496 0.07415 13.4864 0.11415 8.7605 40.3772 4.6090 1.6010 0.6246 0.06655 15.0258 0.10655 9.3851 47.2477 5.0343 1.6651 0.6006 0.06014 16.6268 0.10014 9.9856 54.4546 5.4533 1.7317 0.5775 0.05467 18.2919 0.09467 10.5631 61.9618 5.8659 1.8009 0.5553 0.04994 20.0236 0.08994 11.1184 69.7355 6.2721 1.8730 0.5339 0.04582 21.8245 0.08582 11.6523 77.7441 6.6720 1.9479 0.5134 0.04220 23.6975 0.08220 12.1657 85.9581 7.0656 2.0258 0.4936 0.03899 25.6454 0.07899 12.6593 94.3498 7.4530 2.1068 0.4746 0.03614 27.6712 0.07614 13.1339 102.8933 7.8342 2.1911 0.4564 0.03358 29.7781 0.07358 13.5903 111.5647 8.2091 2.2788 0.4388 0.03128 31.5692 0.07128 14.0292 120.3414 8.5779 TABLE 15 Discrete Cash Flow: Compound Interest Factors 10% Single Payments Uniform Series Payments Arithmetic Gradients Compound Present Sinking Compound Capital Present Gradient Gradient Amount Worth Fund Amount Recovery Worth Present Worth Uniform Series F/P P/F A/F F/A A/P P/A P/G A/G 1.1000 0.9091 1.00000 1.0000 1.10000 0.9091 1.2100 0.8264 0.47619 2.1000 0.57619 1.7355 0.8264 0.4762 1.3310 0.7513 0.30211 3.3100 0.40211 2.4869 2.3291 0.9356 1.4641 0.6830 0.21547 4.6410 0.31547 3.1699 4.3781 1.3812 1.6105 0.6209 0.16380 6.1051 0.26380 3.7908 6.8618 1.8101 1.7716 0.5645 0.12961 7.7156 0.22961 4.3553 9.6842 2.2236 1.9487 0.5132 0.10541 9.4872 0.20541 4.8684 12.7631 2.6216 2.1436 0.1665 0.08744 11.4359 0.18744 5.3349 16.0287 3.0045 2.3579 0.4241 0.07364 13.5795 0.17364 5.7590 19.4215 3.3724 2.5937 0.3855 0.06275 15.9374 0.16275 6.1446 22.8913 3.7255 10% n 1 2 3 4 5 6 7 8 9 10