请完成普通年金终值公式F＝A· [（1＋i）n－1 ]/i ，普通年金现值公式P＝A·[1－（1＋i）

终值：设每年的支付金额为A，利率为i，期数为n，则按复利计算的普通年金终值S为：　S=A%2BA×(1%2Bi)%2BA(1%2Bi)2%2B…%2BA×(1%2Bi)n-1，　等式两边同乘以(1%2Bi)： S(1%2Bi)=A(1%2Bi)%2BA(1%2Bi)2%2B…%2BA(1%2Bl)n(n等均为次方), 上式两边相减可得：S(1%2Bi)-S=A(1%2Bl)n-A, S=A[(1%2Bi)n-1]/i。式中[(1%2Bi)n-1]/i的为普通年金、利率为i，经过n期的年金终值记作(S/A，i,n),可查普通年金终值系数表。同样的可以推导现值： PA =A/(1%2Bi)1%2BA/(1%2Bi)2%2BA/(1%2Bi)3%2B…%2BA/(1%2Bi)n 推导得出：PA =A[1-(1%2Bi)-n]/i 式中，[1-(1%2Bi)-n]/i是普通金为1元、利率为i、经过n期的年金现值，称为现值系数。A为年金数额；i为利息率；n为计息期数；PA为年金现值。

2020-09-20

你好，可以站在普通年金的角度去思考，普通年金是年末支付，而预付年金是年初支付，相比较普通年金，预付年金的期数就比普通年金少一期，因为年初先支付。

2020-09-08

同学，你好我写了拍给你

2021-01-31

您好，您理解一下这个推导过程设每年的支付金额为A，利率为i，期数为n，则按复利计算的年金终值F为:F=A%2BAx(1%2Bi)%2B...%2B Ax(1%2Bi)n-1 等式两边同乘以(1%2Bi): F(1%2Bi)=A(1%2Bi)1%2BA(1%2Bi)2%2B ...%2BA(1%2Bl)n,(n等均为次方) 上式两边相减可得: F(1%2Bi)-F=A(1%2Bi)n-A,F=A[(1%2Bi)n-1]/i

2023-12-27