Question

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Show that the equal payment series compounding factor is (1+i)N-1] F=AL

Answer 1

ANSWER: > EQUAL SERIES PAYMENT COMPOUND FACTOR : when the equal amounts of money woe invested out each time period for certam (M) number of time periods out interest Date of ☺) is called as the coual payment sexles compounding fuctor (F). → For example If a person is able to deposit A amount of dollars every year, with that person gets'percent interest and he can repeat the same procedure for 'n years At end of the nith year, the amount that person wall have is. cq -- poco 3 F=9 Figure : uniform secies compound Amount factor. -> NOW , future value of the first investment occused at time period z is Alitijo! which is one period after present time. Hence it is n-1 periods before the nth Period and then to the power of (n-D.

- In the similour foushion, Putuse value of and amestment occured at time pospod 2 is = A[i+1)=2 » Future value of laust mvestment is - A (1+ign-n= A (1) = A,, Hence by adding all the future values we get c incitenda Alitoa toine+A>0 → on both sides, multiply with CI+) FC1+1) = [A(1+7)!+ AC1+7)^2+---+a] CI+i) = À C1+5h + AC1+5).4 AC175) 7.- +ACiti) Therefore, substract equations © and (3) F(1+0)-F = (A CI+98 + AC147)*+ Acitih... ta Ci+in] – [A(1+977 actor F+Fi-F = A (1+i) + Acitynl+A (1+) 72.+ AC1+) – AC1+34) - ACH+on? ..-A > Fi = A (1+)-A fi = A (+5)-1] = All Citignan

- Therefore FEAS c * In our Question = Ni there is no a difference, I just used small Lecte the equal payment series can also be written aus F=A* Flap, ni p as Flasin = [ litijº_1]