# A formula for how to compound interest, please?

Asked by gailcalled (54570) January 3rd, 2007
I have a tax-free Vanguard Mutual bond fund that is now producing c. %.0377 interest now. How do I figure out the extra little bit generated by compounding over 12 months?
Observing members: 0 Composing members: 0

How often the interest rate is compounded?... it could be compounding weekly or monthly or annually ... If I remember "continuous compounding" is a little more tricky, but generally it should be pretty straightforward.
ben (8568)
F = P(1 + i)^n
ben (8568)
where p is principal, n is number of compoundings, and i is the rate per compounding
ben (8568)
Does that little inverted carat mean (l i) to the nth power? I'll call Vanguard and ask someone about frequency.
gailcalled (54570)
Thanks, Ben.
gailcalled (54570)
* (l i).....
gailcalled (54570)
plus sign on Mac OS platform didn't show up either time. ??
gailcalled (54570)
yes ^ (carat) means to the nth power... and plus signs don't show up from an internal bug... we'll fix that soon.
ben (8568)
finkelitis (1907)
That gives the formula for continuously compounded interest. And e=2.7183 approximately.
finkelitis (1907)
Daniel and Benj, your formulae are different.. and why did the constant "e" show up? I have a fancy hand calculator that does powers, but have lost the instructions. Can one of you figure it out for me when P = \$15,000, i=.0377 and n is 56 weeks? If you're too busy, I'll find a teenager around here to do it. Or is there a Mac mini- application?
gailcalled (54570)
Never mind. I found the scientfic calculator Mac gave me and worked it out. Good teaching w. your mouths shut, guys!
gailcalled (54570)
e is used to calculate continuous interest rate - the idea is that the interest rate is calculated "all the time" - (1+1/n)^n=e
taxlover (21)
when n-->infinity
taxlover (21)
So: lim(1-i/n)^n-1=e^i-1, and eventually - the continuous interest - Ic=e^i-1
taxlover (21)
and that is how e showed up...
taxlover (21)
Thanks, I think. My days of struggling w. calculus and a few advanced colllege math courses are long gone, except in my nightmares. I get the definition of e conceptually but have long forgotten about limits...but I appreciate the effort. We will be snowed in tomorrow. Maybe I'll go back to a text book.
gailcalled (54570)

A= P(1+r/n)^nt

A=Amount
P=Principal
r=interest rate (decimal)
n=number of times compounded
t=time (years)

winblowzxp (498)

@Win: Thanks. I got the answer last year but still appreciate your having bothered.

gailcalled (54570)

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