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?
$1,671.74
$17,028.75
$1,710.61
$8,140.92
The formula to calculate the amount in an account with continuous compounding is given by:
A = P * e^(rt)
Where:
A = the amount in the account after time t
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
t = time in years
Plugging in the given values:
A = 500 * e^(0.082 * 15)
Using a scientific calculator or math software to calculate e^(0.082 * 15), we find that it is approximately 4.844.
A = 500 * 4.844 ≈ $2,422
Therefore, you will have approximately $2,422 in the account after 15 years.
None of the provided answer options are correct.