Question
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?
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.
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.
Answers
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
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