Exponential Growth/Decay & Compound Interest

Front

What is exponential growth?

Back

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

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential decay?

Back

The formula is A = P(1 - r)^t, where A is the final amount, P is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What does 'compounded monthly' mean in finance?

Back

Compounded monthly means that interest is calculated and added to the principal balance every month.

Front

How do you calculate compound interest?

Back

Compound interest can be calculated using the formula 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.

Tags

CCSS.HSF.BF.A.2

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 and also on the accumulated interest from previous periods.

Tags

CCSS.HSF.BF.A.2

Front

If a population decreases by 5% per year, how do you calculate the population after a certain number of years?

Back

Use the formula A = P(1 - r)^t, where P is the initial population, r is the decay rate (0.05 for 5%), and t is the number of years.

Tags

CCSS.HSF-LE.A.1C

Front

What is depreciation in the context of finance?

Back

Depreciation is the reduction in the value of an asset over time, often due to wear and tear or obsolescence.

Tags

CCSS.8.EE.C.7B

Front

How do you find the total amount after compound interest is applied?

Back

The total amount can be found using the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.