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

What does 'e' represent in the continuous compounding formula?

Back

The mathematical constant e is approximately equal to 2.71828 and is the base of the natural logarithm.

Front

Convert 10% to a decimal.

Back

0.1

Front

Convert 25% to a decimal.

Back

0.25

Front

Convert 6% to a decimal.

Back

0.06

Front

What does the 'P' stand for in the formula A = Pe^(rt)?

Back

Initial amount (the principal amount).

Front

If Nick deposits $20,000 at a continuous compounding rate of 2.5%, what will he have after 4 years?

Back

$22,103.42

Front

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

Back

Increasing the interest rate will result in a higher amount accumulated over time.

Front

What is the effect of increasing the time period on the amount accumulated with continuous compounding?

Back

Increasing the time period will also result in a higher amount accumulated due to the compounding effect.

Front

How do you calculate the amount after continuous compounding?

Back

Use the formula A = Pe^(rt). Substitute P for the principal, r for the interest rate, and t for the time in years.