What is continuous interest used for?

Question

It's a formula that uses natural base e.

Answer 1

There's a good math explanation here http://id.mind.net/~zona/mmts/functionInstitute/exponentialFunctions/continuousInterest.html

The idea is that the more often you compound interest, the more money you make. (Or if you're paying, the less you pay. I'll talk about what you get)

The formula for compounding interest is S = P*(1+ i)^n

i is the interest rate per period = r/n ( r/12 for monthly, r/52 for weekly, r/365 for yearly, r/8760 for hourly, etc. )

Turns out that as n goes up, i goes down, but S (the amount you get) goes up. Through some complex math, somebody showed that if you made n get infinitely large, your return would be as big as it could ever get. they found the formula is S = P e^rt. R is the APR and t is expressed in years.

Continuous interest is the upper limit on the amount you can earn from any investment -- no matter how often you compound interest. It probably is used in some Economics formulas that are way beyond most of us. I've never heard of any real interest being compounded continuously, but I've not heard all the crazy things banks do. I can't think of a real use except to satisfy somebody's curiosity.

Answer 2

It's used to calculate future worth of bonds that are compunded continually rather than at some fixed period like daily, monthly, yearly. It's been a while, but I think FV = PV/(1 - rho); where rho is the interest rate, PV is the present value (purchase prices), and FV is the future value (sale price).

PV/(1 - rho) can be derived from the series sum = PV + PVrho^2 + PVrho^3 + ... + PVrho^n; where n --> infinity.