Answer:
P = $2366.91
(maybe try answering without a comma)
Explanation:
The formula for continuous compounding is:
A = Pe^(rt)
Where:
A = final amount
P = principal amount (initial deposit)
e = Euler's number (approximately 2.71828)
r = annual interest rate (as a decimal)
t = time (in years)
We are given:
r = 6.5% = 0.065 (annual interest rate)
t = 12 years
A = $5000 (final amount)
So we can rearrange the formula to solve for P:
P = A / e^(rt)
Substituting the values:
P = 5000 / e^(0.065*12)
P = $2366.91 (rounded to the nearest cent)
Therefore, you would need to deposit $2366.91 in an account with a 6.5% interest rate, compounded continuously, to have $5000 in your account 12 years later.