Exponential Growth/Decay & Compound Interest

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

Define compound interest.

Back

Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

If you invest $1,000 at an annual interest rate of 5% compounded annually for 3 years, how much will you have?

Back

A = 1000(1 + 0.05/1)^(1*3) = $1,157.63.

Front

What does it mean for interest to be compounded quarterly?

Back

Compounding quarterly means that interest is calculated and added to the principal four times a year.

Front

How do you convert a percentage increase to a growth factor?

Back

To convert a percentage increase to a growth factor, add 1 to the percentage expressed as a decimal. For example, a 35% increase becomes 1 + 0.35 = 1.35.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has already been added.

Front

If a population of 10,000 decreases by 4% per year, what is the population after 2 years?

Back

Population = 10000(1 - 0.04)^2 = 9,616.

Front

What is the formula for exponential decay?

Back

y = a(1 - r)^t, where y is the final amount, a is the initial amount, r is the decay rate, and t is time.