What concept describes how quickly an investment increases in value when...

JENNI

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...interest is paid not only on the orig? present value
future value
compound interest
real rate of interest
 
Compound interest is the reason the investment increases in value so quickly
 
Of those, it would be "compound interest".

When there are multiple payments that are regular, it's determined by the summation of a geometric series which you learned in junior high (now middle school). For example if you deposited $100 at the end of the year for three years at 7% interest you would have:

FV = $100 * 1.07^2 + $100 * 1.07^1 + $100

The first term being the first deposit, the second for the second and the last being the third on the target date. Each of these terms is known as the compound interest equation for that payment which is FV = X * ( 1 + Rg )^t, note this is often incorrectly written as FV = X * ( 1 + Rg / n )^( t * n) where n is the number of compounding intervals in a year, this is what you'll find as the compound interest equation. This second formula though taught is wrong and requires Rg to be a "nominal" rate extrapolated from the rate determined by n, for example the compounded monthly rate if n = 12, this is due to the mathematicaly incorrect but commonly used method of annualizing a rate to an annual rate by the multiplication of the rate by how many intervals of that rate there are in a year. You'll notice that this is really the geometric sequence of:

FV = summation of $100 * 1.07^k for k from 0 to 2

The summation of a finite geometric sequence of the term a * r^k for k from 0 to n is a * ( 1 - r^(n+1) ) / ( 1 - r ) therefore you have:

FV = $100 * ( 1 - 1.07^3 ) / ( 1 - 1.07 )
.:
FV = $321.49

This equation can be further simplified to form the ordinary annuity equation or the compound interest savings equation (as opposed to the individual compound savings equation). Indeed the summation of a finite geometric sequence and the summation of a infinite geometric sequence is the basis of almost all the equations you will encounter in finance such as the net present value equation, the dividend discount model, etc. If you understand the summation of a geometric sequence then you don't need to memorize most of the equations they give you in finance as they are merely simplifications of what you've already learned but most people do not understand from junior high.
 
You didn't finish the question but I'm guessing the question is when interest is paid not only on the original amount but the interest earned.

Ans = compound interest
 
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