# What is the unit of the exponent $t$ in the compound interest formula?

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?

• "Is this correct?" Yes, you are right. – 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
$$A= A_0\left(1+PeriodicRate\right)^{Number Of Periods}$$
$$A = A_0\left(1+\frac rn\right)^{nt}$$,