Compound interest and exponential functions

Front

What is compound interest?

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

How is compound interest calculated?

Back

Compound interest is 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 (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

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

Define exponential growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is A = Pe^(rt), where A is the amount after time t, P is the initial amount, e is the base of the natural logarithm, r is the growth rate, and t is time.

Front

What does it mean for a population to triple in size?

Back

For a population to triple in size means that the final population is three times the initial population.

Front

How do you determine the time it takes for a population to triple at a constant growth rate?

Back

You can determine the time to triple using the formula t = ln(3)/ln(1 + r), where r is the growth rate.

Front

What is depreciation in financial terms?

Back

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

Front

How is the value of an asset calculated after depreciation?

Back

The value of an asset after depreciation can be calculated using the formula V = P(1 - r)^t, where V is the value after t years, P is the initial value, r is the depreciation rate, and t is the number of years.

Front

What is the significance of the interest rate in compound interest?

Back

The interest rate determines how much interest is earned on the principal and affects the total amount accumulated over time.