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

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

Back

Initial amount (Principal).

Front

A new online bank offers a savings account that compounds interest continuously at a rate of 2.5%. If Nick deposits $20,000, what amount should he expect to have after 4 years?

Back

$22,103.42

Front

How do you calculate the amount of money in an account after continuous compounding?

Back

Use the formula A = Pe^(rt).

Front

What is the meaning of 'compounded continuously'?

Back

Interest is calculated and added to the principal at every possible instant.

Front

If Ashleigh has $3,567.91 in an account after 10 years at 4.5% compounded continuously, how much did she start with?

Back

$2,275.

Front

Monthly compounding means how many times a year?

Back

12 times.

Front

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

Back

Higher interest rates lead to a greater amount accumulated over time.

Front

What is the relationship between time and the amount accumulated in continuous compounding?

Back

The longer the time period, the more interest is earned, leading to a higher accumulated amount.