3/22 AMDM: Interest Compounded Continuously

Front

What is the formula for calculating the future value of an investment compounded continuously?

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 (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 'compounded continuously' mean in finance?

Back

Compounded continuously means that interest is calculated and added to the principal balance at every moment, rather than at discrete intervals.

Front

How do you convert a percentage to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 16% becomes 0.16.

Front

If Damara invests $3500 at 9.5% compounded continuously for 7 years, how much will she have in her account after 7 years?

Back

$6,805.72

Front

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

Back

e is approximately equal to 2.71828.

Front

What is the significance of the variable 't' in the formula A = Pe^{rt}?

Back

The variable 't' represents the time in years that the money is invested or borrowed.

Front

If the total amount in a savings account is given by the formula A=3250e^{0.062t}, what was the initial amount deposited?

Back

$3,250

Tags

CCSS.HSF.LE.B.5

Front

What is the relationship between the interest rate and the growth of an investment compounded continuously?

Back

A higher interest rate (r) results in a greater amount (A) over time, as the interest is calculated continuously.

Front

If Mark invests $3,285 in a retirement account with a fixed annual interest rate of 14.75% compounded continuously, what will the account balance be after 18 years?

Back

$46,729.08