# Thread: Finance/Actuarial question - on the accumulation function

1. ## Finance/Actuarial question - on the accumulation function

Any help is much appreciated!

2. Originally Posted by cirrus74

Any help is much appreciated!
The accumulate value after 10 periods is the sum of all the future value factors, or one unit projected at a given interest. Our interest is both continuous and variable, so an integral is needed for the sum.

$\int _1 ^{10} e^{\delta t} dt$

Can you solve for such an integral?

3. Thank you. I did as you suggested and solved for that function, but the answer comes up to 1.9 which isn't the answer

exp(-ln(20 - 10)+ ln(20-1)) = exp (ln(19/10)) = 19/10

Did I make a mistake somewhere? Also why are the limits not from 0 to 10?

Sorry for double posting.

4. Accumulated value of the continuous annuity is:

$\frac{e^{n\sigma} - 1}{\sigma}$