# Formula for FVoAD with continuous compounding

• Oct 7th 2011, 04:30 AM
dexteronline
Formula for FVoAD with continuous compounding
I gather that future value of ordinary annuity with continuous compounding of interest is calculated as

FV = PMT [e^rt -1]/[e^r-1]

So to find future value of an annuity due with continuous compounding of interest I would multiply the former by an extra interest factor of e^r thus making the formula as

FV = PMT e^r [e^rt -1]/[e^r-1]

Is this correct, the reason I think this may work is since for discrete compounding of interest we multiply the interest factor of (1+i) to the future value of annuity formula as

FV = PMT (1+i) [(1+i)^n - 1]/i

Just a confirmation of the correctness of the formula will suffice
• Oct 7th 2011, 05:50 AM
SpringFan25
Re: Formula for FVoAD with continuous compounding
$\delta$ = continuously compounded rate
$i$ = annually compounded rate

if you are still paying your annuities as annually, rather than continuously, then all you need to do is convert your "continuously compounded" interest rate into a normal one and then use the standard formula.

if you note that $e^\delta = 1+i$ you will see whether or not you have the right answer.

More often the calculation of interest is the value of annuity paid continuously, which is a different concept to what you described above.