Compound and Continuous Interest/Exponential Functions Review

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 continuous interest different from compound interest?

Back

Continuous interest is calculated using the mathematical constant e, and it compounds infinitely over time, while compound interest is calculated at specific intervals.

Front

What formula is used to calculate the future value of an investment with compound interest?

Back

The future value (FV) can be calculated using the formula: FV = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the formula for continuous compounding?

Back

The formula for continuous compounding is A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

How do you calculate the value of an investment that decreases by a certain percentage each year?

Back

To calculate the value of an investment that decreases by a percentage each year, use the formula: FV = P(1 - r)^t, where P is the initial amount, r is the rate of decrease, and t is the number of years.

Front

What does it mean for a value to increase by a percentage each year?

Back

It means that the value grows by that percentage of its current value every year, leading to exponential growth.

Front

How do you round numbers in financial calculations?

Back

In financial calculations, numbers are typically rounded to two decimal places to represent cents.

Front

What is the significance of the number 'e' in continuous growth models?

Back

The number 'e' (approximately 2.718) is the base of the natural logarithm and is used in continuous growth models to represent exponential growth.

Front

What is the initial value in the function y = 15(1.35)^x?

Back

The initial value in the function is $15, which represents the starting amount before any growth occurs.

Front

How do you interpret a percentage decrease in a population or subscription base?

Back

A percentage decrease indicates that the population or subscription base is shrinking by that percentage each year, leading to a lower total over time.