In her College Algebra lectures given at Missouri State University ( available online) , Patti A. Blanton explains ( Lecture 21) how to apply the exponential groth concept to compound interest.

She first gives an easy to understand formula :

A = $A_0$.$\left(1+PeriodicRate\right)^{Number Of Periods}$.

where the periodic rate is the quotient : $\frac{Annual RateOfInterest} {NumberOfCompoundingTimesPerYear}$.

So, for example, if the annual rate of interest is 8% and if interest is compounded every month, the periodic rate is $\frac {0.8} {12}$.

If I invest a capital for 2 years at a given rate ( say 8%, again) compounded monthly, the number of periods is 2 times 12 , that is 24 periods.

After that, Pr. Blanton gives what she call the " textbook formula" :

A = $A_0$ . $\left(1+\frac rn\right)^{nt}$,

but does not derive explicitly the " hard" textbook formula from the previous easy one.

I understand the quotient $\frac rn$. But I do not understand the exponent $nt$.

The only explanation I see is that $t$ is time in year, so that $nt$ represents the total number of periods.

Is this correct?

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    $\begingroup$ "Is this correct?" Yes, you are right. $\endgroup$ – callculus Feb 25 at 17:36

Note that if you would like to invest for $t$ years and the number of compounding periods in a year is $n$, then the $PeriodicRate = \frac rn$ and the total number of period is $Number Of Periods=nt$. Plug them into the simple formula

$A= A_0\left(1+PeriodicRate\right)^{Number Of Periods}$

to obtain

$A = A_0\left(1+\frac rn\right)^{nt}$,

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