Continuously Compounded Interest

Front

What is continuously compounded interest?

Back

Continuously compounded interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods, compounded continuously over time.

Front

What is the formula for continuously compounded interest?

Back

The formula is A = Pe^(rt), 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), and t is the time in years.

Front

If Adam invests $5,208 at an 8% interest rate compounded continuously for 8 years, what will the account balance be?

Back

$9,876.87

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, 3.5% becomes 0.035.

Front

If Damara invests $3,500 at 2% compounded continuously for 5 years, what will she have in her account?

Back

$3,868.10

Front

What is the effect of increasing the interest rate on the amount accumulated in a continuously compounded interest account?

Back

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

Front

What happens to the account balance if the time period is increased while keeping the interest rate constant?

Back

The account balance will increase, as interest is compounded over a longer period.

Front

If Jessica invests $3,948 at a 9% interest rate compounded continuously for 11 years, what will the account balance be?

Back

$10,624.99

Front

What is the principal in the context of continuously compounded interest?

Back

The principal is the initial amount of money invested or loaned before interest.

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.