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CH4 貨幣的時間價值 本章要點 : 1. 複利終值 2. 複利現值 3. 年金終值 4. 年金現值 5. 永續年金 6. 隱含利率 7. 有效利率 單元劇 : 愛因斯坦認為最恐怖的力量小愛在二次大戰期間, 與研究團隊正在研究原子的分裂性, 正值日本軍肆無忌憚侵略他國之際, 連美國老大哥也受殃及, 小愛的團隊終於成功研發出原子彈, 也立即以日本為試攻擊對象 當戰鬥機第一次配載原子彈升空, 選定日本廣島投彈, 好奇的小愛就在安全範圍的航空母艦上觀查原子彈爆發的威力, 當原子彈著地時舜間產生的毁滅力量, 讓在一旁的小兵嚇得目瞪口呆, 並對著小愛說 : 小愛博士, 您說這是不是世界上最強大的力量呢? 小愛轉頭對著小兵眼神凝重的回答 : 不! 世界上還有比這更強大的力量 小兵好奇的問小愛說 : 那到底還有什麼東西的力量比這原子彈大呢 小愛回答說 : 那就是 複利! 小兵此時一頭霧水地向小愛說 : 小愛博士啊, 您別開玩笑了吧, 我看一枚小小原子彈的威力, 就快把日本給滅了, 您說這不是世界上最強大的力量嗎? 怎麼會是 什麼 利 什麼 複利來的? 小愛博士您快說啊 那到底是什麼東西啊? 當日本軍還搞不懂到底是什麼東西把快半個日本給移為平地時, 日本皇軍嚇得無條件投降 4-1

此時小愛正在甲板上跟小兵討論著什麼是複利, 小愛說 : 古時候有位王員外, 他的家產全是老婆在掌管, 於是他在院子後面挖了個洞, 埋了 100 萬元私房錢, 怕自己老後沒錢還有這筆急用金, 結果日子一久, 當王員外老了時, 埋在院子後的 100 萬竟然壓根給忘了, 等到王員外去世後, 便無人知道王家還有這筆錢 事隔 300 年後, 王家的第十世, 在整修家園中無意發現這筆錢, 結果這筆錢有的還腐蝕了, 完好的部分剩不到 50 萬 小兵說 : 好可惜喔! 接著小愛又說 : 從前也有一個年輕人, 他將自己的第一份工資 1,000 元給存在銀行, 從此之後這年輕人的支出剛好都等於所賺的錢, 再也沒有存錢到這家銀行了, 時間一久, 年輕人卻忘了在銀行還有 1,000 元的存款 一樣事隔約 300 年後, 這年輕人的第十世子孫, 意外發現祖先的存摺, 結果到銀行確認後, 行員告知這存摺裡現在有 22 億多元的存款, 年輕人的後代因此成為爆發戶 小愛說 : 你說複利的力量是不是比原子彈大呢! 小兵又目瞪口呆的回答說 : 是 是 是, 我要趕快去存錢了, 造福我的第十世子孫 4-2

4.1 複利終值 複利終值 = 本金 + 貨幣時間價值 = 本金 (1+ 利率 ) 貨幣時間價值 = 複利終值 - 本金 例 4-1:100 元存放 5 年後會變成多少?( 利率 5%) Ans: 複利終值 5 =100 (1+5%) =127.63 時間價值 =127.63-100=27.63 複利終值公式 : n FV=PV (1+ i%) = PV FVIF( i%,n) (4-1) 符號定義 : FV: 複利終值 (Future Value) PV: 本金, 即現值 (Present value) i %: 利率 (interest) n: 期數 FVIF( i %,n) : 終值利率因子 (Future Value Interest Factor), 可查表 例 4-2:100 元存放 5 年後會變成多少?( 利率 5%) Ans: 100 (1+5%) (1+5%) (1+5%) (1+5%) (1+5%) =100 (1+5%) 100 FVIF(5%,5) 1001.2763 127.63 5 4-3

4.2 複利現值 定義 : 未來期一筆錢在今天的價值 例 4-3: 你現在大二, 再兩年後當你畢業時父母會給你 10 萬元創業金, 請問那 10 萬元在大二的你值多少, 即為現值 ( 折現 ) 的概念 做法 : 現在跟銀行借一筆錢, 金額為 PV, 銀行給你的貸款利率為 i %, 借了 n 年, 則到時候要還銀行的錢為 FV 可將此關係表示為 : PV (1 i%) n FV 符號定義 : PV: 本金, 即現值 (Present value) FV: 複利終值 (Future Value) i %: 利率 (interest) n: 期數 因為你知道畢業後會有 10 萬元, 因此代入數字後 ( 假設銀行貸款利率為 3%): 2 PV (1 3%) 10萬 求未知數 PV: 10萬 PV (1+3%) 2 =94,259.59 意味著可向銀行貸的錢是 94,259.59 元, 等到兩年後要還銀行 10 萬元, 恰好可利用父母給的創業金 10 萬元來償還 亦即兩年後的 10 萬元, 在利率為 3% 的情況下之現值 ( 或折現 ) 為 94,259.59 元 4-4

複利現值公式 : FV PV (1 i%) n 1 FV (1 i %) n FV PVIF(%, i n) (4-2) 符號定義 : PVIF(i %,n) 現值利率因子 (Present Value Interest Factor), 可查表 PV: 本金, 即現值 (Present value) FV: 複利終值 (Future Value) i %: 利率 (interest) n: 期數 例 4-4: 兩年後的 10 萬元, 在市場上利率為 3% 下, 其現值為何? 100, 000 PV 2 (1 3%) 100,000 PVIF(3%,2) 100,000 0.9426 94,260 4.3 年金終值 ( 普通年金終值 ) 定義 : 每經過一等長時間將產生等額現金支付或收取之最終價值 圖示 : 存 100 存 100 存 100 存 100 存 100 0 1 2 3 4 5 現在 年後 年後 年後 年後 年後 總值 = 年金現值 4-5

年金終值公式 : FVA PMT FVIFA(%, i n) (4-3) 符號定義 : FVA: 年金終值 PMT: 年金 FVIFA: 年金終值利率因子 (Future Value Interest Factor of Annuity), 查表 例 4-5: 從現在開始每滿一年就存 10,000, 在市場利率存 5% 的情況下, 維持 10 年後可存多少錢? Ans: PMT FVIFA( i%, n) 10,000 FVIFA(5%,10) 10,00012.578 125,780 證明 : 以例 4-3 證明 1 萬 1 萬 1 萬 1 萬 1 萬 1 萬 1 萬 1 萬 1 萬 1 萬 0 1 2 3 4 5 6 7 8 9 10 FVA PMT (1 i%) PMT (1 i%) PMT (1 i%) PMT (1 i%) 10 1 10 2 10 3 10 10 PMT (1 i%) (1 i%) (1 i%) (1 i%) 10 1 10 2 10 3 10 10 9 8 7 PTM (1 i%) (1 i%) (1 i%) 1 n 11 (1 i%) PMT PMT FVFFA(%, i n) 1 (1 i%) 4-6

補充知識等比級數 : 級數和 (S n)= a1 a2 a n ( 由小到大 ) = a arar ar 2 n 1 1 1 1 1 首項 1-r n (1-r ), r 2 公比, 2 1 = a a 1 a ar 4.4 年金現值 ( 普通年金現值 ) 定義 : 每經過一等長時間將產生等額現金支付或收取之之現在總值 圖示 : 領 100 領 100 領 100 領 100 領 100 0 1 2 3 4 5 現在 年後 年後 年後 年後 年後 總值 = 年金現值 年金現值公式 : PVA PMT PVIFA(%, i n) (4-4) 符號定義 : PVA: 年金現值 PMT: 年金 4-7

PVIFA: 現金現值利率因子 (Present Value Interest Factor of Annuity), 可查表 公式證明 : 同 FVA( 年金終值 ) 例 4-6: 從現在開始每滿一年就可領 10,000 元退休金, 共可領 10 年, 在利率為 5% 下, 請問現在要一次領可以領多少? Ans: PMT PVIFA(%, i n) =10,000PVIFA(5%,10) =10,0007.7217 =77,217 補充 : 1. 期初年金終值 (Future Value Annuity for Due,FVAD) FVAD=PMTFVIFA( (%, i n ))(1+ i % ) (4-5) 符號定義 : FVAD: 期初年金終值 PMT: 年金 FVIFA: 年金終值利率因子 (Future Value Interest Factor of Annuity), 查表 2. 期初年金現值 (Present Value Annuity for Due,PVAD ) PVAD= PMT PVAD ( (%, i n ))(1+ i % ) (4-6) 符號定義 : PVAD: 期初年金現值 PMT: 年金 4-8

PVIFA: 現金現值利率因子 (Present Value Interest Factor of Annuity), 可查表 例 4-7: 同列 4-5, 但 10,000 的年金從今天就開始存, 求此期初年金終值? Ans: FVAD=10,000 FVIFA(5%,10) (1 5%) 10,00012.578 (1 5%) 132,067.87 例 4-8: 同例 4-6, 但此退休金從退休當天即開始領, 則此期初年金現值? Ans: PVAD 10,000 PVIFA(5%,10) (1 5%) 10,0007.7217 (1 5%) 81,077.85 4.5 永續年金現值 (Present Value of Perpetual Annuity, PVPA) 定義 : 一無限期之普通年金現值 公式 : PVPA PMT i% (4-7) 符號定義 : PVPA: 永續年金現值 PMT: 年金 i % : 利率 4-9

PMT PMT PMT 證明 : PVPA 1 2 (1 i%) (1 i%) (1 i%) n 1 1 PMT ( ) 1 2 (1 i%) (1 i%) 1 PMT 1 i% 1 1 1 i % 1 PMT 1 i% 1 i% 1 1 i% PMT i% 1 2 (1+ i%) 1 公比 (r) = 1 1 i% 1 i% 補充知識 : 首項 無窮等比級數和 = 1- 公比 例 4-9: 每滿一年可領 10,000 元, 可領無限期, 請問今天要把這此無限期的每年 10,000 元之年金一次領完, 可折領多少錢?( 利率 =5%) Ans: 10,000 PVPAD= 200,000 5% 4-10

補充 : 期初年金現值 (PVPAD) PMT PVPAD (1 i%) i% (4-8) 4.6 隱含利率 例 4-10: 現在跟銀行借 10,000,3 年後要還 11,000, 請問此借款中所隱含的年利率 ( 隱含利率 ) 是多少? Ans: PV (1 i%) n FV 3 10, 000 (1 i%) 11, 000 3 11, 000 (1 i%) 1.1 10, 000 3 1 i% 1.1 i% 1.03228 1 3.228% 4.7 有效利率 內涵 : 一般利率均是以年為計算基礎, 因此複利滾利的計算是以年為區間, 而有效利率指的是當複利滾利的時間為每年 m 次時, 則此時一年的利率, 我們會稱為有效利率 ( 年化 ) 公式 : i% m 有效利率 = (1 ) 1 (4-9) m 4-11

例 4-11: 在市場利率 ( 年 ) 為 5% 下, 銀行每季計算一次利息, 試問有效利率為何? Ans: 5% 4 有效利率 = (1 ) 1 4 =5.09% 證明 : 本金 (1 i%)= 本利和 i% m 本金 (1 ) = 本利和 m i% m 本金 (1 ) -1 = - m 本利和本金 = 利和 = 貨幣時間價值 i% m 利和 (1 ) -1 = = m 有效利率 本金 4-12

表 1: 複利終值利率因子表 (FVIF) n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 1 1.010 1.015 1.020 1.025 1.030 1.035 1.040 1.045 1.050 1.055 1.060 1.065 1.070 1.075 1.080 1.085 1.090 1.095 1.100 1 2 1.020 1.030 1.040 1.051 1.061 1.071 1.082 1.092 1.103 1.113 1.124 1.134 1.145 1.156 1.166 1.177 1.188 1.199 1.210 2 3 1.030 1.046 1.061 1.077 1.093 1.109 1.125 1.141 1.158 1.174 1.191 1.208 1.225 1.242 1.260 1.277 1.295 1.313 1.331 3 4 1.041 1.061 1.082 1.104 1.126 1.148 1.170 1.193 1.216 1.239 1.262 1.286 1.311 1.335 1.360 1.386 1.412 1.438 1.464 4 5 1.051 1.077 1.104 1.131 1.159 1.188 1.217 1.246 1.276 1.307 1.338 1.370 1.403 1.436 1.469 1.504 1.539 1.574 1.611 5 6 1.062 1.093 1.126 1.160 1.194 1.229 1.265 1.302 1.340 1.379 1.419 1.459 1.501 1.543 1.587 1.631 1.677 1.724 1.772 6 7 1.072 1.110 1.149 1.189 1.230 1.272 1.316 1.361 1.407 1.455 1.504 1.554 1.606 1.659 1.714 1.770 1.828 1.888 1.949 7 8 1.083 1.126 1.172 1.218 1.267 1.317 1.369 1.422 1.477 1.535 1.594 1.655 1.718 1.783 1.851 1.921 1.993 2.067 2.144 8 9 1.094 1.143 1.195 1.249 1.305 1.363 1.423 1.486 1.551 1.619 1.689 1.763 1.838 1.917 1.999 2.084 2.172 2.263 2.358 9 10 1.105 1.161 1.219 1.280 1.344 1.411 1.480 1.553 1.629 1.708 1.791 1.877 1.967 2.061 2.159 2.261 2.367 2.478 2.594 10 11 1.116 1.178 1.243 1.312 1.384 1.460 1.539 1.623 1.710 1.802 1.898 1.999 2.105 2.216 2.332 2.453 2.580 2.714 2.853 11 12 1.127 1.196 1.268 1.345 1.426 1.511 1.601 1.696 1.796 1.901 2.012 2.129 2.252 2.382 2.518 2.662 2.813 2.971 3.138 12 13 1.138 1.214 1.294 1.379 1.469 1.564 1.665 1.772 1.886 2.006 2.133 2.267 2.410 2.560 2.720 2.888 3.066 3.254 3.452 13 14 1.149 1.232 1.319 1.413 1.513 1.619 1.732 1.852 1.980 2.116 2.261 2.415 2.579 2.752 2.937 3.133 3.342 3.563 3.797 14 15 1.161 1.250 1.346 1.448 1.558 1.675 1.801 1.935 2.079 2.232 2.397 2.572 2.759 2.959 3.172 3.400 3.642 3.901 4.177 15 16 1.173 1.269 1.373 1.485 1.605 1.734 1.873 2.022 2.183 2.355 2.540 2.739 2.952 3.181 3.426 3.689 3.970 4.272 4.595 16 17 1.184 1.288 1.400 1.522 1.653 1.795 1.948 2.113 2.292 2.485 2.693 2.917 3.159 3.419 3.700 4.002 4.328 4.678 5.054 17 18 1.196 1.307 1.428 1.560 1.702 1.857 2.026 2.208 2.407 2.621 2.854 3.107 3.380 3.676 3.996 4.342 4.717 5.122 5.560 18 19 1.208 1.327 1.457 1.599 1.754 1.923 2.107 2.308 2.527 2.766 3.026 3.309 3.617 3.951 4.316 4.712 5.142 5.609 6.116 19 20 1.220 1.347 1.486 1.639 1.806 1.990 2.191 2.412 2.653 2.918 3.207 3.524 3.870 4.248 4.661 5.112 5.604 6.142 6.727 20 21 1.232 1.367 1.516 1.680 1.860 2.059 2.279 2.520 2.786 3.078 3.400 3.753 4.141 4.566 5.034 5.547 6.109 6.725 7.400 21 22 1.245 1.388 1.546 1.722 1.916 2.132 2.370 2.634 2.925 3.248 3.604 3.997 4.430 4.909 5.437 6.018 6.659 7.364 8.140 22 23 1.257 1.408 1.577 1.765 1.974 2.206 2.465 2.752 3.072 3.426 3.820 4.256 4.741 5.277 5.871 6.530 7.258 8.064 8.954 23 24 1.270 1.430 1.608 1.809 2.033 2.283 2.563 2.876 3.225 3.615 4.049 4.533 5.072 5.673 6.341 7.085 7.911 8.830 9.850 24 25 1.282 1.451 1.641 1.854 2.094 2.363 2.666 3.005 3.386 3.813 4.292 4.828 5.427 6.098 6.848 7.687 8.623 9.668 10.835 25 26 1.295 1.473 1.673 1.900 2.157 2.446 2.772 3.141 3.556 4.023 4.549 5.141 5.807 6.556 7.396 8.340 9.399 10.587 11.918 26 27 1.308 1.495 1.707 1.948 2.221 2.532 2.883 3.282 3.733 4.244 4.822 5.476 6.214 7.047 7.988 9.049 10.245 11.593 13.110 27 28 1.321 1.517 1.741 1.996 2.288 2.620 2.999 3.430 3.920 4.478 5.112 5.832 6.649 7.576 8.627 9.818 11.167 12.694 14.421 28 29 1.335 1.540 1.776 2.046 2.357 2.712 3.119 3.584 4.116 4.724 5.418 6.211 7.114 8.144 9.317 10.653 12.172 13.900 15.863 29 30 1.348 1.563 1.811 2.098 2.427 2.807 3.243 3.745 4.322 4.984 5.743 6.614 7.612 8.755 10.063 11.558 13.268 15.220 17.449 30 31 1.361 1.587 1.848 2.150 2.500 2.905 3.373 3.914 4.538 5.258 6.088 7.044 8.145 9.412 10.868 12.541 14.462 16.666 19.194 31 32 1.375 1.610 1.885 2.204 2.575 3.007 3.508 4.090 4.765 5.547 6.453 7.502 8.715 10.117 11.737 13.607 15.763 18.250 21.114 32 33 1.389 1.634 1.922 2.259 2.652 3.112 3.648 4.274 5.003 5.852 6.841 7.990 9.325 10.876 12.676 14.763 17.182 19.983 23.225 33 34 1.403 1.659 1.961 2.315 2.732 3.221 3.794 4.466 5.253 6.174 7.251 8.509 9.978 11.692 13.690 16.018 18.728 21.882 25.548 34 35 1.417 1.684 2.000 2.373 2.814 3.334 3.946 4.667 5.516 6.514 7.686 9.062 10.677 12.569 14.785 17.380 20.414 23.960 28.102 35 36 1.431 1.709 2.040 2.433 2.898 3.450 4.104 4.877 5.792 6.872 8.147 9.651 11.424 13.512 15.968 18.857 22.251 26.237 30.913 36 37 1.445 1.735 2.081 2.493 2.985 3.571 4.268 5.097 6.081 7.250 8.636 10.279 12.224 14.525 17.246 20.460 24.254 28.729 34.004 37 38 1.460 1.761 2.122 2.556 3.075 3.696 4.439 5.326 6.385 7.649 9.154 10.947 13.079 15.614 18.625 22.199 26.437 31.458 37.404 38 39 1.474 1.787 2.165 2.620 3.167 3.825 4.616 5.566 6.705 8.069 9.704 11.658 13.995 16.785 20.115 24.086 28.816 34.447 41.145 39 40 1.489 1.814 2.208 2.685 3.262 3.959 4.801 5.816 7.040 8.513 10.286 12.416 14.974 18.044 21.725 26.133 31.409 37.719 45.259 40 41 1.504 1.841 2.252 2.752 3.360 4.098 4.993 6.078 7.392 8.982 10.903 13.223 16.023 19.398 23.462 28.354 34.236 41.303 49.785 41 42 1.519 1.869 2.297 2.821 3.461 4.241 5.193 6.352 7.762 9.476 11.557 14.083 17.144 20.852 25.339 30.764 37.318 45.227 54.764 42 43 1.534 1.897 2.343 2.892 3.565 4.390 5.400 6.637 8.150 9.997 12.250 14.998 18.344 22.416 27.367 33.379 40.676 49.523 60.240 43 44 1.549 1.925 2.390 2.964 3.671 4.543 5.617 6.936 8.557 10.546 12.985 15.973 19.628 24.098 29.556 36.217 44.337 54.228 66.264 44 45 1.565 1.954 2.438 3.038 3.782 4.702 5.841 7.248 8.985 11.127 13.765 17.011 21.002 25.905 31.920 39.295 48.327 59.379 72.890 45 46 1.580 1.984 2.487 3.114 3.895 4.867 6.075 7.574 9.434 11.739 14.590 18.117 22.473 27.848 34.474 42.635 52.677 65.020 80.180 46 47 1.596 2.013 2.536 3.192 4.012 5.037 6.318 7.915 9.906 12.384 15.466 19.294 24.046 29.936 37.232 46.259 57.418 71.197 88.197 47 48 1.612 2.043 2.587 3.271 4.132 5.214 6.571 8.271 10.401 13.065 16.394 20.549 25.729 32.182 40.211 50.191 62.585 77.961 97.017 48 49 1.628 2.074 2.639 3.353 4.256 5.396 6.833 8.644 10.921 13.784 17.378 21.884 27.530 34.595 43.427 54.457 68.218 85.367 106.719 49 50 1.645 2.105 2.692 3.437 4.384 5.585 7.107 9.033 11.467 14.542 18.420 23.307 29.457 37.190 46.902 59.086 74.358 93.477 117.391 50 n/i 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 9.50% 10.00% i/n 4-13

表 2: 複利現值利率因子表 (PVIF) n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 1 0.990 0.985 0.980 0.976 0.971 0.966 0.962 0.957 0.952 0.948 0.943 0.939 0.935 0.930 0.926 0.922 0.917 0.913 0.909 1 2 0.980 0.971 0.961 0.952 0.943 0.934 0.925 0.916 0.907 0.898 0.890 0.882 0.873 0.865 0.857 0.849 0.842 0.834 0.826 2 3 0.971 0.956 0.942 0.929 0.915 0.902 0.889 0.876 0.864 0.852 0.840 0.828 0.816 0.805 0.794 0.783 0.772 0.762 0.751 3 4 0.961 0.942 0.924 0.906 0.888 0.871 0.855 0.839 0.823 0.807 0.792 0.777 0.763 0.749 0.735 0.722 0.708 0.696 0.683 4 5 0.951 0.928 0.906 0.884 0.863 0.842 0.822 0.802 0.784 0.765 0.747 0.730 0.713 0.697 0.681 0.665 0.650 0.635 0.621 5 6 0.942 0.915 0.888 0.862 0.837 0.814 0.790 0.768 0.746 0.725 0.705 0.685 0.666 0.648 0.630 0.613 0.596 0.580 0.564 6 7 0.933 0.901 0.871 0.841 0.813 0.786 0.760 0.735 0.711 0.687 0.665 0.644 0.623 0.603 0.583 0.565 0.547 0.530 0.513 7 8 0.923 0.888 0.853 0.821 0.789 0.759 0.731 0.703 0.677 0.652 0.627 0.604 0.582 0.561 0.540 0.521 0.502 0.484 0.467 8 9 0.914 0.875 0.837 0.801 0.766 0.734 0.703 0.673 0.645 0.618 0.592 0.567 0.544 0.522 0.500 0.480 0.460 0.442 0.424 9 10 0.905 0.862 0.820 0.781 0.744 0.709 0.676 0.644 0.614 0.585 0.558 0.533 0.508 0.485 0.463 0.442 0.422 0.404 0.386 10 11 0.896 0.849 0.804 0.762 0.722 0.685 0.650 0.616 0.585 0.555 0.527 0.500 0.475 0.451 0.429 0.408 0.388 0.369 0.350 11 12 0.887 0.836 0.788 0.744 0.701 0.662 0.625 0.590 0.557 0.526 0.497 0.470 0.444 0.420 0.397 0.376 0.356 0.337 0.319 12 13 0.879 0.824 0.773 0.725 0.681 0.639 0.601 0.564 0.530 0.499 0.469 0.441 0.415 0.391 0.368 0.346 0.326 0.307 0.290 13 14 0.870 0.812 0.758 0.708 0.661 0.618 0.577 0.540 0.505 0.473 0.442 0.414 0.388 0.363 0.340 0.319 0.299 0.281 0.263 14 15 0.861 0.800 0.743 0.690 0.642 0.597 0.555 0.517 0.481 0.448 0.417 0.389 0.362 0.338 0.315 0.294 0.275 0.256 0.239 15 16 0.853 0.788 0.728 0.674 0.623 0.577 0.534 0.494 0.458 0.425 0.394 0.365 0.339 0.314 0.292 0.271 0.252 0.234 0.218 16 17 0.844 0.776 0.714 0.657 0.605 0.557 0.513 0.473 0.436 0.402 0.371 0.343 0.317 0.292 0.270 0.250 0.231 0.214 0.198 17 18 0.836 0.765 0.700 0.641 0.587 0.538 0.494 0.453 0.416 0.381 0.350 0.322 0.296 0.272 0.250 0.230 0.212 0.195 0.180 18 19 0.828 0.754 0.686 0.626 0.570 0.520 0.475 0.433 0.396 0.362 0.331 0.302 0.277 0.253 0.232 0.212 0.194 0.178 0.164 19 20 0.820 0.742 0.673 0.610 0.554 0.503 0.456 0.415 0.377 0.343 0.312 0.284 0.258 0.235 0.215 0.196 0.178 0.163 0.149 20 21 0.811 0.731 0.660 0.595 0.538 0.486 0.439 0.397 0.359 0.325 0.294 0.266 0.242 0.219 0.199 0.180 0.164 0.149 0.135 21 22 0.803 0.721 0.647 0.581 0.522 0.469 0.422 0.380 0.342 0.308 0.278 0.250 0.226 0.204 0.184 0.166 0.150 0.136 0.123 22 23 0.795 0.710 0.634 0.567 0.507 0.453 0.406 0.363 0.326 0.292 0.262 0.235 0.211 0.189 0.170 0.153 0.138 0.124 0.112 23 24 0.788 0.700 0.622 0.553 0.492 0.438 0.390 0.348 0.310 0.277 0.247 0.221 0.197 0.176 0.158 0.141 0.126 0.113 0.102 24 25 0.780 0.689 0.610 0.539 0.478 0.423 0.375 0.333 0.295 0.262 0.233 0.207 0.184 0.164 0.146 0.130 0.116 0.103 0.092 25 26 0.772 0.679 0.598 0.526 0.464 0.409 0.361 0.318 0.281 0.249 0.220 0.194 0.172 0.153 0.135 0.120 0.106 0.094 0.084 26 27 0.764 0.669 0.586 0.513 0.450 0.395 0.347 0.305 0.268 0.236 0.207 0.183 0.161 0.142 0.125 0.111 0.098 0.086 0.076 27 28 0.757 0.659 0.574 0.501 0.437 0.382 0.333 0.292 0.255 0.223 0.196 0.171 0.150 0.132 0.116 0.102 0.090 0.079 0.069 28 29 0.749 0.649 0.563 0.489 0.424 0.369 0.321 0.279 0.243 0.212 0.185 0.161 0.141 0.123 0.107 0.094 0.082 0.072 0.063 29 30 0.742 0.640 0.552 0.477 0.412 0.356 0.308 0.267 0.231 0.201 0.174 0.151 0.131 0.114 0.099 0.087 0.075 0.066 0.057 30 31 0.735 0.630 0.541 0.465 0.400 0.344 0.296 0.256 0.220 0.190 0.164 0.142 0.123 0.106 0.092 0.080 0.069 0.060 0.052 31 32 0.727 0.621 0.531 0.454 0.388 0.333 0.285 0.244 0.210 0.180 0.155 0.133 0.115 0.099 0.085 0.073 0.063 0.055 0.047 32 33 0.720 0.612 0.520 0.443 0.377 0.321 0.274 0.234 0.200 0.171 0.146 0.125 0.107 0.092 0.079 0.068 0.058 0.050 0.043 33 34 0.713 0.603 0.510 0.432 0.366 0.310 0.264 0.224 0.190 0.162 0.138 0.118 0.100 0.086 0.073 0.062 0.053 0.046 0.039 34 35 0.706 0.594 0.500 0.421 0.355 0.300 0.253 0.214 0.181 0.154 0.130 0.110 0.094 0.080 0.068 0.058 0.049 0.042 0.036 35 36 0.699 0.585 0.490 0.411 0.345 0.290 0.244 0.205 0.173 0.146 0.123 0.104 0.088 0.074 0.063 0.053 0.045 0.038 0.032 36 37 0.692 0.576 0.481 0.401 0.335 0.280 0.234 0.196 0.164 0.138 0.116 0.097 0.082 0.069 0.058 0.049 0.041 0.035 0.029 37 38 0.685 0.568 0.471 0.391 0.325 0.271 0.225 0.188 0.157 0.131 0.109 0.091 0.076 0.064 0.054 0.045 0.038 0.032 0.027 38 39 0.678 0.560 0.462 0.382 0.316 0.261 0.217 0.180 0.149 0.124 0.103 0.086 0.071 0.060 0.050 0.042 0.035 0.029 0.024 39 40 0.672 0.551 0.453 0.372 0.307 0.253 0.208 0.172 0.142 0.117 0.097 0.081 0.067 0.055 0.046 0.038 0.032 0.027 0.022 40 41 0.665 0.543 0.444 0.363 0.298 0.244 0.200 0.165 0.135 0.111 0.092 0.076 0.062 0.052 0.043 0.035 0.029 0.024 0.020 41 42 0.658 0.535 0.435 0.354 0.289 0.236 0.193 0.157 0.129 0.106 0.087 0.071 0.058 0.048 0.039 0.033 0.027 0.022 0.018 42 43 0.652 0.527 0.427 0.346 0.281 0.228 0.185 0.151 0.123 0.100 0.082 0.067 0.055 0.045 0.037 0.030 0.025 0.020 0.017 43 44 0.645 0.519 0.418 0.337 0.272 0.220 0.178 0.144 0.117 0.095 0.077 0.063 0.051 0.041 0.034 0.028 0.023 0.018 0.015 44 45 0.639 0.512 0.410 0.329 0.264 0.213 0.171 0.138 0.111 0.090 0.073 0.059 0.048 0.039 0.031 0.025 0.021 0.017 0.014 45 46 0.633 0.504 0.402 0.321 0.257 0.205 0.165 0.132 0.106 0.085 0.069 0.055 0.044 0.036 0.029 0.023 0.019 0.015 0.012 46 47 0.626 0.497 0.394 0.313 0.249 0.199 0.158 0.126 0.101 0.081 0.065 0.052 0.042 0.033 0.027 0.022 0.017 0.014 0.011 47 48 0.620 0.489 0.387 0.306 0.242 0.192 0.152 0.121 0.096 0.077 0.061 0.049 0.039 0.031 0.025 0.020 0.016 0.013 0.010 48 49 0.614 0.482 0.379 0.298 0.235 0.185 0.146 0.116 0.092 0.073 0.058 0.046 0.036 0.029 0.023 0.018 0.015 0.012 0.009 49 50 0.608 0.475 0.372 0.291 0.228 0.179 0.141 0.111 0.087 0.069 0.054 0.043 0.034 0.027 0.021 0.017 0.013 0.011 0.009 50 n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 4-14

表 3: 年金終值利率因子表 (FVIFA) n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 2 2.010 2.015 2.020 2.025 2.030 2.035 2.040 2.045 2.050 2.055 2.060 2.065 2.070 2.075 2.080 2.085 2.090 2.095 2.100 2 3 3.030 3.045 3.060 3.076 3.091 3.106 3.122 3.137 3.153 3.168 3.184 3.199 3.215 3.231 3.246 3.262 3.278 3.294 3.310 3 4 4.060 4.091 4.122 4.153 4.184 4.215 4.246 4.278 4.310 4.342 4.375 4.407 4.440 4.473 4.506 4.540 4.573 4.607 4.641 4 5 5.10 5.15 5.20 5.26 5.31 5.36 5.42 5.47 5.53 5.58 5.64 5.69 5.75 5.81 5.87 5.93 5.98 6.04 6.11 5 6 6.15 6.23 6.31 6.39 6.47 6.55 6.63 6.72 6.80 6.89 6.98 7.06 7.15 7.24 7.34 7.43 7.52 7.62 7.72 6 7 7.21 7.32 7.43 7.55 7.66 7.78 7.90 8.02 8.14 8.27 8.39 8.52 8.65 8.79 8.92 9.06 9.20 9.34 9.49 7 8 8.29 8.43 8.58 8.74 8.89 9.05 9.21 9.38 9.55 9.72 9.90 10.08 10.26 10.45 10.64 10.83 11.03 11.23 11.44 8 9 9.37 9.56 9.75 9.95 10.16 10.37 10.58 10.80 11.03 11.26 11.49 11.73 11.98 12.23 12.49 12.75 13.02 13.30 13.58 9 10 10.46 10.70 10.95 11.20 11.46 11.73 12.01 12.29 12.58 12.88 13.18 13.49 13.82 14.15 14.49 14.84 15.19 15.56 15.94 10 11 11.57 11.86 12.17 12.48 12.81 13.14 13.49 13.84 14.21 14.58 14.97 15.37 15.78 16.21 16.65 17.10 17.56 18.04 18.53 11 12 12.68 13.04 13.41 13.80 14.19 14.60 15.03 15.46 15.92 16.39 16.87 17.37 17.89 18.42 18.98 19.55 20.14 20.75 21.38 12 13 13.8 14.2 14.7 15.1 15.6 16.1 16.6 17.2 17.7 18.3 18.9 19.5 20.1 20.8 21.5 22.2 23.0 23.7 24.5 13 14 14.9 15.5 16.0 16.5 17.1 17.7 18.3 18.9 19.6 20.3 21.0 21.8 22.6 23.4 24.2 25.1 26.0 27.0 28.0 14 15 16.1 16.7 17.3 17.9 18.6 19.3 20.0 20.8 21.6 22.4 23.3 24.2 25.1 26.1 27.2 28.2 29.4 30.5 31.8 15 16 17.3 17.9 18.6 19.4 20.2 21.0 21.8 22.7 23.7 24.6 25.7 26.8 27.9 29.1 30.3 31.6 33.0 34.4 35.9 16 17 18.4 19.2 20.0 20.9 21.8 22.7 23.7 24.7 25.8 27.0 28.2 29.5 30.8 32.3 33.8 35.3 37.0 38.7 40.5 17 18 19.6 20.5 21.4 22.4 23.4 24.5 25.6 26.9 28.1 29.5 30.9 32.4 34.0 35.7 37.5 39.3 41.3 43.4 45.6 18 19 20.8 21.8 22.8 23.9 25.1 26.4 27.7 29.1 30.5 32.1 33.8 35.5 37.4 39.4 41.4 43.7 46.0 48.5 51.2 19 20 22.0 23.1 24.3 25.5 26.9 28.3 29.8 31.4 33.1 34.9 36.8 38.8 41.0 43.3 45.8 48.4 51.2 54.1 57.3 20 21 23.2 24.5 25.8 27.2 28.7 30.3 32.0 33.8 35.7 37.8 40.0 42.3 44.9 47.6 50.4 53.5 56.8 60.3 64.0 21 22 24.5 25.8 27.3 28.9 30.5 32.3 34.2 36.3 38.5 40.9 43.4 46.1 49.0 52.1 55.5 59.0 62.9 67.0 71.4 22 23 25.7 27.2 28.8 30.6 32.5 34.5 36.6 38.9 41.4 44.1 47.0 50.1 53.4 57.0 60.9 65.1 69.5 74.4 79.5 23 24 27.0 28.6 30.4 32.3 34.4 36.7 39.1 41.7 44.5 47.5 50.8 54.4 58.2 62.3 66.8 71.6 76.8 82.4 88.5 24 25 28.2 30.1 32.0 34.2 36.5 38.9 41.6 44.6 47.7 51.2 54.9 58.9 63.2 68.0 73.1 78.7 84.7 91.2 98.3 25 26 29.5 31.5 33.7 36.0 38.6 41.3 44.3 47.6 51.1 55.0 59.2 63.7 68.7 74.1 80.0 86.4 93.3 100.9 109.2 26 27 30.8 33.0 35.3 37.9 40.7 43.8 47.1 50.7 54.7 59.0 63.7 68.9 74.5 80.6 87.4 94.7 102.7 111.5 121.1 27 28 32.1 34.5 37.1 39.9 42.9 46.3 50.0 54.0 58.4 63.2 68.5 74.3 80.7 87.7 95.3 103.7 113.0 123.1 134.2 28 29 33.5 36.0 38.8 41.9 45.2 48.9 53.0 57.4 62.3 67.7 73.6 80.2 87.3 95.3 104.0 113.6 124.1 135.8 148.6 29 30 34.8 37.5 40.6 43.9 47.6 51.6 56.1 61.0 66.4 72.4 79.1 86.4 94.5 103.4 113.3 124.2 136.3 149.7 164.5 30 31 36.1 39.1 42.4 46.0 50.0 54.4 59.3 64.8 70.8 77.4 84.8 93.0 102.1 112.2 123.3 135.8 149.6 164.9 181.9 31 32 37.5 40.7 44.2 48.2 52.5 57.3 62.7 68.7 75.3 82.7 90.9 100.0 110.2 121.6 134.2 148.3 164.0 181.6 201.1 32 33 38.9 42.3 46.1 50.4 55.1 60.3 66.2 72.8 80.1 88.2 97.3 107.5 118.9 131.7 146.0 161.9 179.8 199.8 222.3 33 34 40.3 43.9 48.0 52.6 57.7 63.5 69.9 77.0 85.1 94.1 104.2 115.5 128.3 142.6 158.6 176.7 197.0 219.8 245.5 34 35 41.7 45.6 50.0 54.9 60.5 66.7 73.7 81.5 90.3 100.3 111.4 124.0 138.2 154.3 172.3 192.7 215.7 241.7 271.0 35 36 43.1 47.3 52.0 57.3 63.3 70.0 77.6 86.2 95.8 106.8 119.1 133.1 148.9 166.8 187.1 210.1 236.1 265.6 299.1 36 37 44.5 49.0 54.0 59.7 66.2 73.5 81.7 91.0 101.6 113.6 127.3 142.7 160.3 180.3 203.1 228.9 258.4 291.9 330.0 37 38 46.0 50.7 56.1 62.2 69.2 77.0 86.0 96.1 107.7 120.9 135.9 153.0 172.6 194.9 220.3 249.4 282.6 320.6 364.0 38 39 47.4 52.5 58.2 64.8 72.2 80.7 90.4 101.5 114.1 128.5 145.1 164.0 185.6 210.5 238.9 271.6 309.1 352.1 401.4 39 40 48.9 54.3 60.4 67.4 75.4 84.6 95.0 107.0 120.8 136.6 154.8 175.6 199.6 227.3 259.1 295.7 337.9 386.5 442.6 40 41 50.4 56.1 62.6 70.1 78.7 88.5 99.8 112.8 127.8 145.1 165.0 188.0 214.6 245.3 280.8 321.8 369.3 424.2 487.9 41 42 51.9 57.9 64.9 72.8 82.0 92.6 104.8 118.9 135.2 154.1 176.0 201.3 230.6 264.7 304.2 350.2 403.5 465.5 537.6 42 43 53.4 59.8 67.2 75.7 85.5 96.8 110.0 125.3 143.0 163.6 187.5 215.4 247.8 285.6 329.6 380.9 440.8 510.8 592.4 43 44 54.9 61.7 69.5 78.6 89.0 101.2 115.4 131.9 151.1 173.6 199.8 230.4 266.1 308.0 356.9 414.3 481.5 560.3 652.6 44 45 56.5 63.6 71.9 81.5 92.7 105.8 121.0 138.8 159.7 184.1 212.7 246.3 285.7 332.1 386.5 450.5 525.9 614.5 718.9 45 46 58.0 65.6 74.3 84.6 96.5 110.5 126.9 146.1 168.7 195.2 226.5 263.3 306.8 358.0 418.4 489.8 574.2 673.9 791.8 46 47 59.6 67.6 76.8 87.7 100.4 115.4 132.9 153.7 178.1 207.0 241.1 281.5 329.2 385.8 452.9 532.5 626.9 738.9 872.0 47 48 61.2 69.6 79.4 90.9 104.4 120.4 139.3 161.6 188.0 219.4 256.6 300.7 353.3 415.8 490.1 578.7 684.3 810.1 960.2 48 49 62.8 71.6 81.9 94.1 108.5 125.6 145.8 169.9 198.4 232.4 273.0 321.3 379.0 447.9 530.3 628.9 746.9 888.1 1057.2 49 50 64.5 73.7 84.6 97.5 112.8 131.0 152.7 178.5 209.3 246.2 290.3 343.2 406.5 482.5 573.8 683.4 815.1 973.4 1163.9 50 n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 4-15

表 4: 年金現值利率因子表 (PVIFA) n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 1 0.990 0.985 0.980 0.976 0.971 0.966 0.962 0.957 0.952 0.948 0.943 0.939 0.935 0.930 0.926 0.922 0.917 0.913 0.909 1 2 1.970 1.956 1.942 1.927 1.913 1.900 1.886 1.873 1.859 1.846 1.833 1.821 1.808 1.796 1.783 1.771 1.759 1.747 1.736 2 3 2.941 2.912 2.884 2.856 2.829 2.802 2.775 2.749 2.723 2.698 2.673 2.648 2.624 2.601 2.577 2.554 2.531 2.509 2.487 3 4 3.902 3.854 3.808 3.762 3.717 3.673 3.630 3.588 3.546 3.505 3.465 3.426 3.387 3.349 3.312 3.276 3.240 3.204 3.170 4 5 4.853 4.783 4.713 4.646 4.580 4.515 4.452 4.390 4.329 4.270 4.212 4.156 4.100 4.046 3.993 3.941 3.890 3.840 3.791 5 6 5.795 5.697 5.601 5.508 5.417 5.329 5.242 5.158 5.076 4.996 4.917 4.841 4.767 4.694 4.623 4.554 4.486 4.420 4.355 6 7 6.728 6.598 6.472 6.349 6.230 6.115 6.002 5.893 5.786 5.683 5.582 5.485 5.389 5.297 5.206 5.119 5.033 4.950 4.868 7 8 7.652 7.486 7.325 7.170 7.020 6.874 6.733 6.596 6.463 6.335 6.210 6.089 5.971 5.857 5.747 5.639 5.535 5.433 5.335 8 9 8.566 8.361 8.162 7.971 7.786 7.608 7.435 7.269 7.108 6.952 6.802 6.656 6.515 6.379 6.247 6.119 5.995 5.875 5.759 9 10 9.471 9.222 8.983 8.752 8.530 8.317 8.111 7.913 7.722 7.538 7.360 7.189 7.024 6.864 6.710 6.561 6.418 6.279 6.145 10 11 10.368 10.071 9.787 9.514 9.253 9.002 8.760 8.529 8.306 8.093 7.887 7.689 7.499 7.315 7.139 6.969 6.805 6.647 6.495 11 12 11.255 10.908 10.575 10.258 9.954 9.663 9.385 9.119 8.863 8.619 8.384 8.159 7.943 7.735 7.536 7.345 7.161 6.984 6.814 12 13 12.134 11.732 11.348 10.983 10.635 10.303 9.986 9.683 9.394 9.117 8.853 8.600 8.358 8.126 7.904 7.691 7.487 7.291 7.103 13 14 13.004 12.543 12.106 11.691 11.296 10.921 10.563 10.223 9.899 9.590 9.295 9.014 8.745 8.489 8.244 8.010 7.786 7.572 7.367 14 15 13.865 13.343 12.849 12.381 11.938 11.517 11.118 10.740 10.380 10.038 9.712 9.403 9.108 8.827 8.559 8.304 8.061 7.828 7.606 15 16 14.718 14.131 13.578 13.055 12.561 12.094 11.652 11.234 10.838 10.462 10.106 9.768 9.447 9.142 8.851 8.575 8.313 8.062 7.824 16 17 15.562 14.908 14.292 13.712 13.166 12.651 12.166 11.707 11.274 10.865 10.477 10.111 9.763 9.434 9.122 8.825 8.544 8.276 8.022 17 18 16.398 15.673 14.992 14.353 13.754 13.190 12.659 12.160 11.690 11.246 10.828 10.432 10.059 9.706 9.372 9.055 8.756 8.471 8.201 18 19 17.226 16.426 15.678 14.979 14.324 13.710 13.134 12.593 12.085 11.608 11.158 10.735 10.336 9.959 9.604 9.268 8.950 8.650 8.365 19 20 18.046 17.169 16.351 15.589 14.877 14.212 13.590 13.008 12.462 11.950 11.470 11.019 10.594 10.194 9.818 9.463 9.129 8.812 8.514 20 21 18.857 17.900 17.011 16.185 15.415 14.698 14.029 13.405 12.821 12.275 11.764 11.285 10.836 10.413 10.017 9.644 9.292 8.961 8.649 21 22 19.660 18.621 17.658 16.765 15.937 15.167 14.451 13.784 13.163 12.583 12.042 11.535 11.061 10.617 10.201 9.810 9.442 9.097 8.772 22 23 20.456 19.331 18.292 17.332 16.444 15.620 14.857 14.148 13.489 12.875 12.303 11.770 11.272 10.807 10.371 9.963 9.580 9.221 8.883 23 24 21.243 20.030 18.914 17.885 16.936 16.058 15.247 14.495 13.799 13.152 12.550 11.991 11.469 10.983 10.529 10.104 9.707 9.334 8.985 24 25 22.023 20.720 19.523 18.424 17.413 16.482 15.622 14.828 14.094 13.414 12.783 12.198 11.654 11.147 10.675 10.234 9.823 9.438 9.077 25 26 22.795 21.399 20.121 18.951 17.877 16.890 15.983 15.147 14.375 13.662 13.003 12.392 11.826 11.299 10.810 10.354 9.929 9.532 9.161 26 27 23.560 22.068 20.707 19.464 18.327 17.285 16.330 15.451 14.643 13.898 13.211 12.575 11.987 11.441 10.935 10.465 10.027 9.618 9.237 27 28 24.316 22.727 21.281 19.965 18.764 17.667 16.663 15.743 14.898 14.121 13.406 12.746 12.137 11.573 11.051 10.566 10.116 9.697 9.307 28 29 25.066 23.376 21.844 20.454 19.188 18.036 16.984 16.022 15.141 14.333 13.591 12.907 12.278 11.696 11.158 10.660 10.198 9.769 9.370 29 30 25.808 24.016 22.396 20.930 19.600 18.392 17.292 16.289 15.372 14.534 13.765 13.059 12.409 11.810 11.258 10.747 10.274 9.835 9.427 30 31 26.542 24.646 22.938 21.395 20.000 18.736 17.588 16.544 15.593 14.724 13.929 13.201 12.532 11.917 11.350 10.827 10.343 9.895 9.479 31 32 27.270 25.267 23.468 21.849 20.389 19.069 17.874 16.789 15.803 14.904 14.084 13.334 12.647 12.015 11.435 10.900 10.406 9.950 9.526 32 33 27.990 25.879 23.989 22.292 20.766 19.390 18.148 17.023 16.003 15.075 14.230 13.459 12.754 12.107 11.514 10.968 10.464 10.000 9.569 33 34 28.703 26.482 24.499 22.724 21.132 19.701 18.411 17.247 16.193 15.237 14.368 13.577 12.854 12.193 11.587 11.030 10.518 10.045 9.609 34 35 29.409 27.076 24.999 23.145 21.487 20.001 18.665 17.461 16.374 15.391 14.498 13.687 12.948 12.273 11.655 11.088 10.567 10.087 9.644 35 36 30.108 27.661 25.489 23.556 21.832 20.290 18.908 17.666 16.547 15.536 14.621 13.791 13.035 12.347 11.717 11.141 10.612 10.125 9.677 36 37 30.800 28.237 25.969 23.957 22.167 20.571 19.143 17.862 16.711 15.674 14.737 13.888 13.117 12.415 11.775 11.190 10.653 10.160 9.706 37 38 31.485 28.805 26.441 24.349 22.492 20.841 19.368 18.050 16.868 15.805 14.846 13.979 13.193 12.479 11.829 11.235 10.691 10.192 9.733 38 39 32.163 29.365 26.903 24.730 22.808 21.102 19.584 18.230 17.017 15.929 14.949 14.065 13.265 12.539 11.879 11.276 10.726 10.221 9.757 39 40 32.835 29.916 27.355 25.103 23.115 21.355 19.793 18.402 17.159 16.046 15.046 14.146 13.332 12.594 11.925 11.315 10.757 10.247 9.779 40 41 33.500 30.459 27.799 25.466 23.412 21.599 19.993 18.566 17.294 16.157 15.138 14.221 13.394 12.646 11.967 11.350 10.787 10.271 9.799 41 42 34.158 30.994 28.235 25.821 23.701 21.835 20.186 18.724 17.423 16.263 15.225 14.292 13.452 12.694 12.007 11.382 10.813 10.294 9.817 42 43 34.810 31.521 28.662 26.166 23.982 22.063 20.371 18.874 17.546 16.363 15.306 14.359 13.507 12.739 12.043 11.412 10.838 10.314 9.834 43 44 35.455 32.041 29.080 26.504 24.254 22.283 20.549 19.018 17.663 16.458 15.383 14.421 13.558 12.780 12.077 11.440 10.861 10.332 9.849 44 45 36.095 32.552 29.490 26.833 24.519 22.495 20.720 19.156 17.774 16.548 15.456 14.480 13.606 12.819 12.108 11.465 10.881 10.349 9.863 45 46 36.727 33.056 29.892 27.154 24.775 22.701 20.885 19.288 17.880 16.633 15.524 14.535 13.650 12.855 12.137 11.489 10.900 10.364 9.875 46 47 37.354 33.553 30.287 27.467 25.025 22.899 21.043 19.415 17.981 16.714 15.589 14.587 13.692 12.888 12.164 11.510 10.918 10.378 9.887 47 48 37.974 34.043 30.673 27.773 25.267 23.091 21.195 19.536 18.077 16.790 15.650 14.636 13.730 12.919 12.189 11.530 10.934 10.391 9.897 48 49 38.588 34.525 31.052 28.071 25.502 23.277 21.341 19.651 18.169 16.863 15.708 14.682 13.767 12.948 12.212 11.549 10.948 10.403 9.906 49 50 39.196 35.000 31.424 28.362 25.730 23.456 21.482 19.762 18.256 16.932 15.762 14.725 13.801 12.975 12.233 11.566 10.962 10.414 9.915 50 n/i 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% i/n 4-16