# Finance/Actuarial question - on the accumulation function

• April 9th 2008, 03:59 AM
cirrus74
Finance/Actuarial question - on the accumulation function
• April 9th 2008, 04:48 AM
colby2152
Quote:

Originally Posted by cirrus74

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?
• April 9th 2008, 01:41 PM
cirrus74
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 (Shake)

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.
• April 9th 2008, 08:23 PM
mathceleb
Accumulated value of the continuous annuity is:

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