个人住房贷款还款算法及推导方法

:1999212215:,200137:F8301572:100627388(2000)0120028205:A:,:;;;,,,,,,,,,,,,,,1(),(),,,,,,,,,,,,,,:A=iõ(1+i)n(1+i)n-1õY,Y,()n,i,k,A:::8220001123kn1kn(1)Y,,,:Yõ(1+i)n1(2),,:k,A,kA:Aõ(1+i)n-kk1n,:Aõ(1+i)n-1+Aõ(1+i)n-2++A=Aõnk=1(1+i)n-k2(3)():nõA323:Aõnk=1(1+i)n-k-nõA4(4)::Yõ(1+i)n-Aõnk=1(1+i)n-k-nõA5(5):=nõA5,:Yõ(1+i)n=Aõnk=1(1+i)n-k6(6)6:nk=1(1+i)n-k:nk=1(1+i)n-k=1õ1-(1+i)n1-(1+i)=(1+i)n-1i7(7)76():A=iõ(1+i)n(1+i)n-1õY8=Aõn=iõ(1+i)n(1+i)n-1õYõn9(8)k():K=iõ(1+i)n(1+i)n-1õYõk10:89102,,,92(),,,ww,,,:,wY,()n,i,k,A,t,G(G,),n=w+tõv,:w(),vt:w,tw=0,w;tw0,:k1nww+tkw+2tw+vtAA+GA+2GA+vG(1)kFw,F0F0=Aõwk=1(1+i)n-k-wõA=Aõ(1+i)n-w[(1+i)w-1]i-Aõw1(2)kw,FF=(A+G)t+wk=w+1(1+i)n-k-tõ(A+G)]+[(A+2G)2t+wk=w+t+1(1+i)n-k-tõ(A+2G)++[(A+võG)nk=w+(v-1)õt+1(1+i)n-k-tõ(A+vG)]22:t+wk=w+1(1+i)n-k=(1+i)n-(w+1)+(1+i)n-(w+2)++(1+i)n-(t+w)=(1+i)n-(w+t)õ1-(1+i)t1-(1+i)=(1+i)n-(w+t)õ[(1+i)t-1]i32t+wk=w+t+1(1+i)n-k=(1+i)n-(w+2t)õ[(1+i)t-1]i4vt+wk=w+(v-1)t+1(1+i)n-k=(1+i)n-(w+vt)õ[(1+i)t-1]i=(1+i)t-1i5(1)2,F,:Sm=a1+2a1d+3a1d2++ma1dm-1Smd=a1d+2a1d2+3a1d3++ma1dm6Sm-Smd=a1+a1d+a1d2++a1dm-1-ma1dm7:Sm(1-d)=a1(1-dm)1-d-ma1dm=a1[1-dm-mdm+mdm+1]1-dSm=a1[1-(1+m)dm+mdm+1](1-d)28,80320001F1=Aõ(1+i)n-(w+1)õ[(1+i)t-1]i++(1+i)n-(w+vt)õ[(1+i)t-1]i=[(1+i)tV-1]iõ(1+i)n-(w+vt)õA=[(1+i)tV-1]iõA9(2)F:F=F1+F2+F3+F4.2345:F2=G(1+i)n-(w+t)õ[(1+i)t-1]i+2G(1+i)n-(w+2t)õ[(1+i)t-1]i++vG(1+i)n-(w+vt)õ[(1+i)t-1]i10F2=Gõ(1+i)t-1iõ(1+i)n-(t+w)õ(1+i)2tõ[1-(1+v)(1+i)-tv+võ(1+i)-t(v+1)][(1+i)t-1]2=Gõ(1+i)n+t-wõ[1-(1+v)(1+i)-tv+v(1+i)-t(v+1)]i[(1+i)t-1]11F3=-tõAõv12F4=-t(G+2G++vG)=-tv(v+1)G213(1):Y(1+i)n-F0-F1-F2-F3-F4=tõvõA+v(1+v)õtõG2+wõA14F0F1F2:F0+F1=Yõ(1+i)n-F2-wõA[(1+i)n-w[(1+i)w-1]+[(1+i)tõv-1]õAi=Yõ(1+i)n-G(1+i)n+t-w[1-(1+v)õ(1+i)-tv+v(1+i)-tõ(v+1)]iõ[(1+i)t-1]1515A:A=iõ(1+i)nY(1+i)n-w[(1+i)w-1]+[(1+i)tõv-1]-G(1+i)n+t-w[1-(1+v)(1+i)-tõv+v(1+i)-tõ(v+1)][(1+i)t-1]õ(1+i)n-w[(1+i)w-1]+[(1+i)tõv-1]16()AõkkwAõw+intk-wt+1intk-wtõtõG2+tõAõintk-wt+A+intk-wt+1õGõk-tõintk-wt-wkw17:v=0,n=w,16:,wY,()n,i,k,A,t,G(G,),n=w+tõv,,w(),wA+vG,vt13:w,:tw=0,w;tw0A():A=iõYõ(1+i)n[(1+i)w-1]+[(1+i)n-vt]õ[(1+i)tõv-1]-Gõ(1+i)n[1-võ(1+i)-tõ(v-1)+(v-1)õ(1+i)-tõV]+võ[(1+i)w-1]õ[(1+i)t-1][(1+i)t-1]õ[(1+i)w-1]+[(1+i)n-vt]õ[(1+t)tõv-1]():AõkktAõtõint(kt)+int(kt)-1int(kt)õtõG2+k-tõint(kt)õ[A+int(k-wt)õG]tkvtvõtõA+(v-1)õvõtõG2+(k-vt)õA+(k-vt)õvõGkvtv=0,n=w,:,wwb,A,t()G;G0,G=0,G0Y,i,n,n=wb+tõv+we,:1wbn,t0,v0n-wbt,0wet,:A=Yi(1+i)n(1+i)n-1-G(1+i)n-1[(1+i)we(1+i)(v+1)t-1(1+i)t-1-(v+1)]:(a)(G0)AYõiGYi(1+i)we(1+i)(v+1)t-1(1+i)t-1-(v+1)(b)(G0):G-Yi(1+i)n(1+i)n-1(v+1)-1(1+i)n-1[(1+i)we(1+i)(v+1)t-1(1+i)t-1-(v+1)]3wb,A,t()s:s0,s=0,s0Y,i,n,n=wb+tõv+we,1wbn,t0,v0n-wbt,0wet,:(1)1+s(1+i)t:A=Yi(1+i)n(1+i)vt+we[(1+i)wb-1]+(1+s)[(1+i)t-1](1+i)we(1+i)vt-(1+s)v(1+i)t-(1+s)+(1+s)v+1[(1+i)we-1](2)1+s=(1+i)t():2320001A=Yi((1+i)n(1+s)v{[(1+i)wb+(v+1)s](1+i)we-(1+s)}(3)::AYõi,:-1s04,,Y,n,i,k,:=Yn,k=Yn+(1-k-1n)õYõi=(1-kn)õY,=knõY+k-(k-1)k2nõYõi=k-(k-1)k2nõYõi5,6,;,,Y,n,:=Yn[:],,,,,,,,,,,,,,,,,,;,,;,,,,,,,6%,25%30%,()33