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1、1 期末付年金期初付年金现值终值现值终值标准型1nnvia(1)1nniia1nnvis(1)1nnids变动利率年金111(1)tnntssai1110(1)tnnn stssi1110(1)tnntssai111(1)tnnn stssi付款频率低于计息频率2nkkknkkavvvs21(1)(1)n knknksiis21kkn knkavvva(1)(1)(1)nn knkisiia付款频率低于计息频率的永续年金21kkkkavvsis211kkkkavvaia付款频率高于计息频率121()()11()nmnmnmmmmnmvavvvvi()()()1(1)(1)nnmmmnniisa
2、i1()()()1(1)nmmmmnnviaad1()()()1(1)(1)nmmmmnniissd付款频率高于计息频率的永续年金()()1mmai()()1mmad连续年金01nntnvdtav00(1)1(1)(1)nnnn tsnidtdsiis()()1limlimnmmnnnmmvaaa()()(1)1limlimnmmnnnmmisss各年付款额成等差数列期末现值：232(0)()(2)(1)nnnnvVPvPQ vPQ vPnQ vPQiaa期末终值：()(0)(1)nnnnV nViPQiss期末现值：(0)(0)(1)nnnnvVViPQdaa期末终值：()(0)(1)nnn
3、nV nViPQdss各年付款额成等差数列P=1 Q=1 时1()nnnnnnnvnviiiaavIa1(1)(1)()()nnnnniisIsIa(1)()()nnnnnvidaIaIa(1)()()nnnnnidsIsIa各年付款额成等差数列P=n Q=-1 时()nnnnnnviian aDana(1)(1)()()nnnnnniiisDsDa(1)()()nnnidn aDaDa(1)(1)()()nnnnnniidsDsDa各年付款额成等比数列211(0)(1)(1)1()1nnnVvvkvkikki(1)(1)()(0)(1)nnnikV nviik1(0)(0)(1)()(1)1
4、()1nVViikiki(1)(1)()(0)(1)()(1)nnnikV nViiki2 更一般年金付款频率小于计息频率2(1)(0)2(1)kkmkmknnkkVmmnvkvvvvaais()(0)(1)nnkknkV nVisais(0)(0)(1)nnkknvkVViaads()(0)(1)nnkknkV nVisads更一般年金付款频率小于计息频率每计息期 m 次付款相等12()1121121211()1()2()()()mmmnmmnnnnnmmmmmnmIavvvvvvanvvvvi()()()(1)()()mmnnmnnnisIsIai1()()()(1)()()nmmnmmn
5、nianvIaIad()()()(1)()()mmnnmnnnisIsIad更一般年金付款频率小于计息频率每计息期 m 次付款等差12()1121121211()()12()()122()(1)1(1)2()()mmmnmmnnnmmmnnmmmnmnmnmmmmnmnmnmnmnmnmnmnmnmavvvIvvvvvvanvi()()()()()()(1)()()mmmnnmnnnmmsisaIIi()1()()()()()(1)()()mnmmnmmnnmmianvaaIId()()()()()()(1)()()mmmnnmnnnmmsisaIId虹式年金nnaa2(1)nnnnnaaiss(1)nnnnaaiaa(1)nnnnssiss连续变化年金0()nntnanvtdtIav付款额随时间变化以f(t)形式给出0(0)()ntVf tdtv利息强度也随时间变化00(0)()nsndsVf tdte