Question
Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years?
(1 point)
Responses
$1,671.74
$1,671.74
$17,028.75
$17,028.75
$1,710.61
$1,710.61
$8,140.92
(1 point)
Responses
$1,671.74
$1,671.74
$17,028.75
$17,028.75
$1,710.61
$1,710.61
$8,140.92
Answers
GPT 3.5
To calculate the amount you will have in the account after 15 years, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the amount in the account after time t
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time in years
e = the mathematical constant approximately equal to 2.71828
In this case, P = $500, r = 8.2% = 0.082 (as a decimal), and t = 15 years.
Substituting the values into the formula:
A = 500 * e^(0.082 * 15)
Using a calculator:
A ≈ $1,671.74
Therefore, you will have approximately $1,671.74 in the account after 15 years.
The correct answer is:
$1,671.74
A = P * e^(rt)
Where:
A = the amount in the account after time t
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time in years
e = the mathematical constant approximately equal to 2.71828
In this case, P = $500, r = 8.2% = 0.082 (as a decimal), and t = 15 years.
Substituting the values into the formula:
A = 500 * e^(0.082 * 15)
Using a calculator:
A ≈ $1,671.74
Therefore, you will have approximately $1,671.74 in the account after 15 years.
The correct answer is:
$1,671.74