$10000 is deposited in an account earning 8% interest compounded continuously.

Question

Use the continuous interest formula below to determine how long it takes for the amount in the account to double. A=Pe^rt.

Round answer to 2 decimal places.

____ Years?

Answer 1

2 = e^.08t

ln2 = .08t

t = ln2/.08

t = about 8.66 years doubling time

in about 8.66 years for $10,000 doubling to $20,000 at 8% interest compounded continuously

Answer 2

The formula for continuous compounding is given as A = Pe^rt, where A is the amount in the account at time t, P is the initial deposit (in this case, $10,000), r is the interest rate (in this case, 8%), and t is the time elapsed. To determine how long it takes for the amount in the account to double, we can set A equal to 2P and solve for t:

2P = Pe^rt 2P/P = Pe^rt/P 2 = e^rt

Taking the natural logarithm of both sides:

ln 2 = rt t = ln 2 / r

Plugging in the values from the problem:

t = ln 2 / 0.08 t = 8.68 years

Rounding to 2 decimal places:

t = 8.68 years

So it would take approximately 8.68 years for the $10,000 deposit to double with continuous compounding at an interest rate of 8%.