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
The formula for continuous compounding is given by:
A = P * e^(rt)
where:
A = amount of money accumulated after n years, including interest
P = principal amount (the initial deposit)
r = annual interest rate (in decimal form)
t = number of years the money is invested for
e = Euler's number, approximately equal to 2.71828
Plugging in the values:
r = 8.2% = 0.082
t = 15 years
P = $500
A = $500 * e^(0.082*15)
A ≈ $1710.61
So, after 15 years, you would have $1,710.61 in the account.