Question

Describe the relationship between compound interest and exponential growth

Answer 1

The relationship between compound interest and exponential growth involves an initial amount growing by a fixed percentage over time. Both the GDP growth and savings growth can be calculated using the same compound formula, where even small rate changes can have large effects over time.

Step-by-step explanation:

Relationship Between Compound Interest and Exponential Growth

The relationship between compound interest and exponential growth is closely linked, as both concepts involve growth that accumulates at an increasing rate over time. Compound interest on financial savings is the interest earned not only on the initial principal but also on the accumulated interest from previous periods. This is akin to exponential growth where a quantity increases by a fixed percentage over each time interval, leading to growth that builds upon itself. The formulas for compound interest and compound growth rates are essentially the same. They consist of an initial amount, a rate of growth or interest rate, and a time period over which the growth or interest is applied.

For example, both the growth of a country's Gross Domestic Product (GDP) and the growth of financial savings can utilize the compound interest formula. An original amount (GDP or financial savings), a percentage increase (GDP growth rate or interest rate), and a time period are the elements involved for calculation.

Even small changes in the percentage rate can result in significant differences over an extended time frame, similar to productivity rates, showing how compound interest and growth can have powerful effects on income and economies.

Answer 2

Relationship between compound interest and exponential growth

C.I =
`P[(1 + (R)/(100))^(n) - 1]`

where, P =Principal

R =Rate of interest, n= Duration i.e time interval for which money has been taken, C.I =Compound Interest

Exponential growth = A
`(1+(K)/(100))^s`

Where , A=Initial value of population, K= Rate at which population is declining in percentage, s=total time between starting population and final population

Now , If you compare between Exponential growth and compound interest

P→(Replaced by)→A,

R→(Replaced by)→K,

n→(Replaced by)→s,

As C.I is calculated for money, and Exponential word is used for both money as well as increase in population.

So, just replacing keeping the meaning same

C.I =
`P[(1 + (R)/(100))^(n)]` - P

→Compound Interest = Exponential growth - Initial Value(either money or any population considered)