Table VII. Compound Interest Table Amount of One Dollar Principal with Compound Interest at Various Rates. 1$1.025 $1.030 $1.035 $1.040 $1.045 $1.050 $1.055 $1.060 $1.065 $1.070 $1.800 2 1.051 1.061 1.071 1.082 1.092 1.103 3 1.077 1.093 1.109 1.125 1.141 1.158 4 1.104 1.126 1.148 1.170 1.193 1.131 1.159 1.188 1.217 1.246 1.113 1.174 1.124 1.134 1.145 1.166 1.191 1.208 1.225 1.260 1.216 1.239 1.262 1.286 1.311 1.360 1.276 1.307 1.338 1.370 1.403 1.469 8.982 10.903 13.223 16.023 23.462 9.476 11.557 14.083 17.144 25.339 9.997 12.250 14.998 18.344 27.367 41 2.752 3.360 4.098 4.993 6.078 7.392 42 2.821 3.461 4.241 5.193 6.352 7.762 43 2.892 3.565 4.390 5.400 6.637 8.150 44 2.964 3.671 4.543 5.617 6.936 8.557 10.547 12.985 15.973 19.628 29.556 45 3.038 3.782 4.702 5.841 7.248 8.985 11.127 13.765 17.011 21.002 31.920 46 3.114 3.895 4.867 6.075 7.574 9.434 11.739 14.590 18.117 22.473 34.474 47 3.192 4.012 5.037 6.318 7.915 9.906 12.384 15.466 19.294 24.046 37.232 48 3.271 4.132 5.214 6.571 8.271 10.401 13.065 16.394 20.549 25.729 40.211 49 3.353 4.256 5.396 6.833 8.644 10.921 13.784 17.378 21.884 27.530 43.427 50 3.437 4.384 5.585 7.107 9.033 11.467 14.542 18.420 23.307 29.457 46.902 91,192 721 47 23 56789 15 96,285 735 40 78,106 765 94,818 94,089 19 93,362 725 20 92,637 723 45 74,173 828 70 21 91,914 722 46 73,345 848 72,497 870 72 90,471 720 48 71,627 896 73 31,243 2,505 24 89,751 719 49 70,731 927 74 28,738 2,501 76,567 785 75,782 797 68 812 69 26 25 89,032 718 50 88,314 718 51 69,804 27 29 87,596 718 52 66,797 1,091 78 18,961 2,291 65,706 1,143 79 16,670 2,196 65 68,842 1,001 67,841 1,044 77 21,330 2,369 962 75 26,237 2,476 76 23,761 2,431 Table IX. Heights and Weights of Men Light-face figures are 20 per cent. under and over the average. Ft. In. 5 0 96 100 102 105 106 107 107 107 Ft. 120 125 128 131 133 134 134 134 5 144 150 154 157 160 161 161 161 98 101 103 105 107 109 109 109 122 126 129 131 134 136 136 136 146 151 155 157 161 163 163 163 99 102 105 106 109 110 110 110)] 2 124 128 131 133 136 138 138 138 149 154 157 160 163 166 166 166 102 105 107 109 111 113 113 113 3 127 131 134 136 139 141 141 141 152 157 161 163 167 169 169 169 105 108 110 112 114 115 116 116 131 135 138 140 143 144 145 145 6 157 162 166 168 172 173 174 174 107 110 113 114 117 118 119 119 5 134 138 141 143 146 147 149 149| 161 166 169 172 175 176 179 179 110 114 116 118 120 121 122 122 6 138 142 145 147 150 151 153 153 166 170 174 176 180 181 184 184 114 118 120 122 124 125 126 126 7 142 147 150 152 155 156 158 158 170 176 180 182 186 187 190 190 8 In. 117 121 123 126 128 129 130 130 146 151 154 157 160 161 163 163 175 181 185 188 192 193 196 196 120 124 127 130 132 133 134 134 9 150 155 159 162 165 166 167 168 180 186 191 194 198 199 200 202 123 127 131 134 136 137 138 138 10 154 159 164 167 170 171 172 173 185 191 197 200 204 205 206 2081 127 131 135 138 140 142 142 142 11 159 164 169 173 175 177 177 178 191 197 203 208 210 212 212 214 132 136 140 143 144 146 146 146 0 165 170 175 179 180 183 182 183 198 204 210 215 216 220 218 220 136 142 145 148 149 151 150 151 1 170 177 181 185 186 189 188 189 204 212 217 222 223 227 226 227 141 147 150 154 155 157 155 155 2 176 184 188 192 194 196 194 194 211 221 226 230 233 235 233 233 145 152 156 160 162 163 161 158 3 181 190 195 200 203 204 201 198 217 228 234 240 244 245 241 238 55-60 EXPLANATION OF TABLE II* VALUES AND LOGARITHMS OF TRIGONOMETRIC FUNCTIONS 1. DIRECT READING OF THE VALUES. This table gives the sines, cosines, tangents and cotangents of the angles from 0° to 45°; and by a simple device, indicated by the printing, the values of these functions for angles from 45° to 90° may be read directly from the same table. For angles less than 45° read down the page, the degrees and minutes being found on the left; for angles greater than 45° read up the page the degrees and minutes being found on the right. = To find a function of an angle (such as 15° 27', for example) we employ the process of interpolation. To illustrate, let us find tan 15° 27'. In the table we find tan 15° 20' .2742 and tan 15° 30' = .2773; we know that tan 15° 27' lies between these two numbers. The process of interpolation depends on the assumption that between 15° 20′ and 15° 30′ the tangent of the angle varies directly as the angle; while this assumption is not strictly true, it gives an approximation sufficiently accurate for a four-place table. Thus we should assume that tan 15° 25' is halfway between .2742 and .2773. We may state the problem as follows: An increase of 10' in the angle increases the tangent .0031; assuming that the tangent varies as the angle, an increase of 7' in the angle will increase the tangent by .7 × .0031 four places we write this .0022. Hence = .00217. tan 15° 27' = .2742.0022 = .2764. Retaining only The difference between two successive values in the table is called the tabular difference (.0031 above). The proportional part of the tabular difference which is used is called the correction (.0022 above), and is found by multiplying the tabular difference by the appropriate fraction (.7 above). tabular difference = .0013 (subtracted mentally from the table). *The use of Table I. is explained on pages 80-86 of the text. (to be subtracted because the cosine decreases as the angle increases). Rule. To find a trigonometric function of an angle by interpolation: select the angle in the table which is next smaller than the given angle, and read its sine (cosine, tangent, or cotangent as the case may be) and the tabular difference. Compute the correction as the proper proportional part of the tabular difference. In case of sines or tangents ADD the correction: in case of cosines or cotangents, SUBTRACT it. 2. REVERSE READINGS. Interpolation is also used in finding the angle when one of its functions is given. Example 1. Given sin x = .3294, to find x. Looking in the table we find the sine which is next less than the given sine to be .3283, and this belongs to 19° 10′. Subtract the value of the sine selected from the given sine to obtain the actual difference note that the tabular difference = .0011; .0028. We may state the problem as follows: an increase of .0028 in the function increases the angle 10'; then an increase of .0011 in the function will increase the angle 11/28 of 10 = 4 (to be added). Hence x = 19° 14'. Example 2. Given cos x = .2900, to find x. The cosine in the table next less than this is .2896 and belongs to 73° 10′; the tabular difference is 28; the actual difference is 4; correction = 4/28 of 10 = 1 (to be subtracted). Hence x = 73° 9'. |