How much Jim can accumulate in a private pension fund over 20 years if the fund offers 5% interest compounded annually, and he can afford to deposit $2,000 at the end of every 2nd year?

Question

My textbook says the correct answer is $32,259, but I can't seem to get the same answer using the (F/A,i,N), etc equivalence factors. Any help would be appreciated.

Answer 1

You don't say what he started with. Assuming $2000, at the end of year 2 he has

2000*1.05^2

at the end of year 4, he has

2000*1.05^4 + 2000*1.05^2

so, after 20 years, that's 10 investments, totaling

2000 (1.05^20 + 1.05^18 + ... + 1.05^2)

Now, 1.05^2 = 1.1025 so that's the same as
2000 (1.1025^10 + ... + 1.1025)
= 2000(1.1025^11 - 1)/(1.1025-1)
= 37566

So, I guess he started with zero, since

2000(1.1025^10 - 1)/(1.1025-1) = 32259