Normally, you have an interest rate, r, over some specified period (typically a month, quarter or year) and an amount Y that is invested (or loaned) for n periods. Then the total value, V, of the investment is:
V = Y*(1 + r/100)^n
It is possible to chop up the total time interval into smaller intervals and adjust the interest rate correspondingly so that the total percentage change over a year remains the same. The above equation then takes the form
V = Y*e^ax
The statement in the question simply means that, instead of calculating the interest using the first formula, it is calculated using the second. The interest is then paid out every three months and so every three months the capital returns to the value Y.
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Yes, it can be either an adjective or adverb. It can mean continuously, or traveled without stopping.
It depends on which compound interest formula you mean. Refer to the Wikipedia Article on "Compound Interest" for the correct terminology.
Continuous compounding is the process of calculating interest and adding it to existing principal and interest at infinitely short time intervals. When interest is added to the principal, compound interest arise.
A Circle if you mean 2d circle, 3d sphere =P Any continuously curves shape has no sides; ellipse (ellipsoid), cone, hyperbolic paraboloid...
RMS is a type of average. It is the "root of the mean of the squares". That is, the individual values are squared, the average is taken, and the square root of this is calculated. Since the "individual values" are often continuous - a typical example is a voltage, which continuously changes for example as a sine wave - integration must be used.