# Annuity

kill(all);  ratprint:false;SIMPSUM:TRUE; numer:TRUE;

FORMULA 3 Annuity

F3B: PV=nusum(avalue/(1+r/Times)^(i*Times/aTimes), i, 1, N*aTimes);

(1)
Given Data: 
 r:0.05, avalue:100, aTimes:1, Times:1, N:10;
Unknown:
 PV;

 val:solve(ev(F3B, r:0.05, avalue:100, aTimes:1, Times:1, N:10),PV);

Graphics: down the line, Saving S[i] to be decreased

S[70]:rhs(val[1]);

ev(for i:71 step 1 thru 80 do(S[i]:S[i-1]*(1+r)-avalue), r:0.05, avalue:100);

data1:makelist([i, S[i]],i,70,80);

FORMULA 1-A compounding

F1A:FV=PV*(1+r/Times)^(n*Times);

FORMULA 3  Morgage

F3A: PV=nusum(rvalue/(1+r/Times)^(i*Times/rTimes), i, 1, N*rTimes);

PV2:solve(ev(F1A, FV:S[70], r:0.05,n:(70-25),rTimes:1, Times:1), PV);

val3:float(ev(solve(F3A, rvalue), PV:rhs(PV2[1]), r:0.05,N:(70-25),rTimes:1, Times:1));

S[26]:rhs(val3[1]);

ev(for i:27 step 1 thru 70 do(S[i]:S[i-1]*(1+r)+avalue), r:0.05, avalue:rhs(val3[1]));

data2:makelist([i, S[i]],i,26,80);

plot2d([discrete, data2]);

Legal Notice: The copyright for this application is owned by the authors.
The authors are not responsible for any errors contained within and are not liable
for any damages resulting from the use of this material.
This application is intended for non-commercial, non-profit use only.
Contact the authors for permission if you wish to use this application in for-profit activities.
Contact address: Prof. Yukari Shirota, Faculty of Economics, Gakushuin University, 1-5-1 Mejiro,
Toshima-ku, Tokyo, 171-8588 JAPAN,  yukari.shirota@ipsj.or.jp