# A formula for how to compound interest, please?

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?

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## 20 Answers

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.

** F = P(1 + i)^n **

where p is principal, n is number of compoundings, and i is the rate per compounding

Does that little inverted carat mean (l i) to the nth power? I'll call Vanguard and ask someone about frequency.

Thanks, Ben.

* (l i).....

plus sign on Mac OS platform didn't show up either time. ??

yes ^ (carat) means to the nth power... and plus signs don't show up from an internal bug... we'll fix that soon.

That gives the formula for continuously compounded interest. And e=2.7183 approximately.

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?

Never mind. I found the scientfic calculator Mac gave me and worked it out. Good teaching w. your mouths shut, guys!

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

when n-->infinity

So: lim(1-i/n)^n-1=e^i-1, and eventually - the continuous interest - Ic=e^i-1

and that is how e showed up...

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.

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

A=Amount

P=Principal

r=interest rate (decimal)

n=number of times compounded

t=time (years)

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

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