as in time value money we get accumulated value and also get accumulated value by annuity we also get accumulated value. what is difference between in both? eg. find accumulated value of 1000 after 10 years @10% 1000(1+0.1)^10 =2594 and by annuity give 1000* [(1+0.1)^10 -1 ]/(0.1) =15937.42 why we dont get same ans as both gives us accumulated value?
The answer differs both because you are accumulating a different amount of capital and over different amount of time. In the first case you have 1000 accumulated for 10 years In the second case you have 10,000 split into ten 1,000 payments accumulated for 9,8,7,6,5,4,3,2,1,0 years (assuming first payment is at t=1, not t=0 - this is what you've calculated anyway) So the amount of capital differs firstly (1,000 vs 10,000) - if we were to set the annuity payments so total capital was 1,000 i.e. ten payments of 100 we would get an accumulated value of 1,593.74 (still less than 2594). The difference remaining here is due to the timing of the cashflows over the ten years rather than all at the beginning.
