Helen deposited $1200 at 5% interest compounded continuously. After 6 years, how much did she have ?
I got $2,160 but I was told it was incorrect
P = Po*e^(r*t).
r*t = 0.05*6 = 0.3.
P = 1200 * e^0.3 = $1619.83.
To calculate the amount Helen had after 6 years with continuous compounding, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial deposit)
e = Euler's number (approximately 2.71828)
r = interest rate (as a decimal)
t = time (in years)
In this case, Helen deposited $1200 at an interest rate of 5%, which is equivalent to a decimal of 0.05. And t = 6 years.
Plugging in the values into the formula:
A = 1200 * e^(0.05 * 6)
To evaluate this expression, we first calculate e^(0.05 * 6) and then multiply it by 1200.
Using a calculator:
e^(0.05 * 6) ≈ 1.3478594
A ≈ 1200 * 1.3478594
A ≈ $1617.4313
So, after 6 years with continuous compounding, Helen would have approximately $1617.43.