If your initial deposit at ECU is $1000, what continuous compound interest rate would ECU need to pay for you to have $1123.60?

Answer 1

Start by writing down th4e formula for continuous compounding:

P(t) = P₀e^rt

In your problem, P(t) = $1123.60, P₀ = $1000, r is the rate we're trying to find, and t is the period that the money's in the bank

$1123.60 = $1000e^rt

$1123.60 / $1000 = e^rt

1.12360 = e^rt

To get the rate, r, out of the exponent take the log base e (ln) of both sides of the equation:

ln(1.12360) = rt

You didn't state what the time period, t, was in the problem. I'm guessing it's 1 year (t = 1):

ln(1.12360) = r

0.1165 = r which is 11.65%