22. Compounding Continuously

Front

What is the formula for continuous compounding?

Back

A = Pe^(rt), 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

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

Back

$2,225.54

Front

Damara invests $3500 at 2% compounded continuously for 5 years. How much will she have in her account after 5 years?

Back

$3,868.10

Front

Convert 25% to a decimal.

Back

0.25

Front

Convert 6% to a decimal.

Back

0.06

Front

What does 'semi-annually' mean in terms of compounding frequency?

Back

It means the interest is compounded 2 times a year.

Front

What is the value of e (Euler's number) approximately?

Back

Approximately 2.71828.

Front

What is the effect of increasing the interest rate on the amount accumulated with continuous compounding?

Back

Increasing the interest rate results in a higher amount accumulated over the same period.

Front

How does continuous compounding differ from annual compounding?

Back

Continuous compounding calculates interest at every possible moment, while annual compounding calculates interest at the end of each year.

Front

What is the principal amount in the formula A = Pe^(rt)?

Back

The principal amount (P) is the initial sum of money invested or loaned.