Unit 4 (4.1-4.3) Flashcard

Front

What is the formula for calculating the future value of an investment with compound interest?

Back

A = P(1 + r)^t, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years.

Front

How do you convert a percentage to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 4% becomes 0.04.

Front

What is continuous compounding in finance?

Back

Continuous compounding refers to the process of earning interest on an investment that is calculated and added to the principal continuously, rather than at discrete intervals. The formula is A = Pe^(rt), where e is the base of the natural logarithm.

Front

What is the half-life of a substance?

Back

The half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in pharmacology and nuclear physics.

Front

How do you calculate the remaining amount of a substance after a certain number of half-lives?

Back

Remaining amount = Initial amount * (1/2)^(number of half-lives). For example, if you start with 500 mg and the half-life is 5 hours, after 20 hours (4 half-lives), the remaining amount is 500 * (1/2)^4 = 31.25 mg.

Front

What is the formula for calculating the amount of an investment after a certain time with continuous compounding?

Back

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

Front

If an object melts at a constant percentage rate, how do you calculate its size after a certain time?

Back

Use the formula: Remaining size = Initial size * (1 - decay rate)^time. For example, if an ice sculpture melts at 3% per minute, after 15 minutes, its height would be 52 * (1 - 0.03)^15.

Front

What is the significance of the number 'e' in continuous compounding?

Back

The number 'e' (approximately 2.71828) is the base of the natural logarithm and is used in the formula for continuous compounding to represent growth that occurs continuously.

Front

How do you determine the future value of an investment compounded annually?

Back

Use the formula A = P(1 + r)^t, where A is the future value, P is the principal, r is the annual interest rate (as a decimal), 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 and also on the accumulated interest from previous periods.