Continuous Compounding + PV

I have spent way too much time trying to wrap my head around this one. So, I decided to reach out to the mighty warriors here on AF.

Q: Your pension plan will pay you a lump sum distribution of $285,000 in 18 months. Assuming continuous compounding at an annual rate of 7%, calculate the present value of the distribution.

First off, I already know how to calculate the present value. I just don’t understand the calculation conceptually. I understand continuous compounding. However, I am confused on the concepts behind this problem specifically. Can somebody help me out on this one please??

All they’re asking is how much you would have to invest today at 7% compounded continuously to have $285,000 in 1½ years.

Makes perfect sense. So how would you go about computing this one on the BA II plus?

$285,000 ÷ (e^(1.5 × 7%)).

You should get $256,592.

Thank you, sir.

I totally get it now. Didn’t realize there was a straight forward formula for PV w/ Continuous Compounding.

PV w/continuous compounding = C ÷ e^rt

C = Cash Flow

r = rate

t = time

http://www.financeformulas.net/Present-Value-Continuous-Compounding.html

You’re quite welcome.

One more thing,

Somehow I get the same answer entering the following on the BAII plus:

(-.07*1.5) = -.105

2nd LN (i.e. e^x) = .9003

.9003*285,000 = $256,592

I noticed that e^(-.105) = 1 ÷(e^(+.105))

What am I missing here? I know this probably goes back to my highschool days but I don’t get it.

You’re not missing anything: e^(-x) = 1/(e^x). That’s one of the rules for exponents.

LOL you are a great encourager. I would say the “rules for exponents” does qualify as going back to my highschool days. Either way, thanks so much for your help tonight. I truly appreciate it. Now I can move on w/o that buggin me for the next 3 days.

My pleasure.