# Continuous Annuity??

• November 15th 2012, 07:43 AM
SgtSmackSmitH
Continuous Annuity??
Hey i know how to figure out annuity annually, semiannualy, quarterly, monthly, and daily. All with the formula

S=R [((1+i)^n -1)/i]

but me and my teacher were wondering if it would be possible to go past daily annuity and go to continuous annuity. So basically "annuity e" i.e the number e. Is this possible??
• November 16th 2012, 01:10 PM
SpringFan25
Re: Continuous Annuity??
yes they are called continuously compounded annuities, and if i remember correctly the formula for the accumulated value is

$\bar{S_n} = \frac{e^{\delta n} -1}{\delta}$

where $\delta = \ln (1+i)$, and i is the annually compounded interest rate.
• November 16th 2012, 01:17 PM
SgtSmackSmitH
Re: Continuous Annuity??
Ok thanks, so if my interest was 6%, 'i' would equal .06 or the yearly rate, correct? And S (subscript n) is what exactly?? Thanks
• November 17th 2012, 05:29 AM
SpringFan25
Re: Continuous Annuity??
Sn is the accumulated value of the continuous annuity after n years.

i is 6% in your example, yes.