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 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 (decimal), n is the number of times that 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 time t, P is the principal amount, r is the annual interest rate (decimal), and e is Euler's number (approximately 2.71828).

Front

What is half-life in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in radioactive decay.

Front

If an investment of $1,500 is compounded at 4% annually, what will be the balance after 5 years?

Back

Using the formula A = P(1 + r/n)^(nt), the balance will be approximately $1,825.51.

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 accumulated interest.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 4.3% becomes 0.043.

Front

What is the effect of compounding frequency on the total amount?

Back

The more frequently interest is compounded, the more interest will be accrued, resulting in a higher total amount.

Front

What is the future value of an investment?

Back

The future value of an investment is the amount of money that an investment will grow to over a period of time at a specified interest rate.

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How do you determine which investment option is better?

Back

To determine which investment option is better, compare the future values of each option after the same period of time.