you deposit 10,000 dollars in an account that pays 4.25% interest compouned continuously. How long will it take for the account balance to reach $15,000?

i have $15,000=$10,000e^(.0425)(t).
is that right? if not please can i get a reasoning if it's wrong, thanks

<<you deposit 10,000 dollars in an account that pays 4.25% interest compouned continuously. How long will it take for the account balance to reach $15,000?

I have $15,000=$10,000e^(.0425)(t). >>

For "coninuous componding" that would be correct, if t is in years.
1.5 = e^0.425t
ln 1.5 = 0.40547 = 0.0425t
t = 9.54 years

yes

now divide both sides by 10000
1.5 = e^(.0425t)
.0425t = ln 1.5
t = 9.54 years

dy/dt = .0425 y

dy/y = .0425 dt
ln y = .0425 t + c
y = e^(.0425 t +c) = e^c e^.0425 t
= C e^.0425 t
at t = 0, y = 10,000 so C = 10,000
y = 10,000 e^.0425 t
so

YES, you are right

1.5 = e^.0425 t
ln 1.5 = .0425 t
.0425 t = .4055
t = 9.54 years

Well, for once we all agree :)

You probably won't find a financial institution declaring a "continuous compounding" interest rate, or doing it that way. The results would be very nearly the same as daily compounding, but, in that case, a different formula would be used.

I suppose they would want to give you back the same amount at 10 am and 2 pm. They only do calculations at night :)

To determine the time it will take for the account balance to reach $15,000, we need to use the formula for compound interest, which is:

A = P * e^(rt)

Where:
A = the final amount (in this case $15,000)
P = the principal amount (in this case $10,000)
e = the mathematical constant approximately equal to 2.71828
r = the interest rate per compounding period (in this case 4.25%, which needs to be converted to a decimal form, so r = 0.0425)
t = the time in years (what we need to find)

Now, let's substitute the given values into the formula:

$15,000 = $10,000 * e^(0.0425t)

To solve for t, we need to isolate it on one side of the equation. Dividing both sides of the equation by $10,000 gives us:

1.5 = e^(0.0425t)

Now, take the natural logarithm (ln) of both sides of the equation:

ln(1.5) = ln(e^(0.0425t))

According to the properties of logarithms, ln(e^(0.0425t)) is equal to 0.0425t, so the equation becomes:

ln(1.5) = 0.0425t

Finally, to solve for t, divide both sides of the equation by 0.0425:

t = ln(1.5) / 0.0425

Using a calculator, you can evaluate ln(1.5) and then divide it by 0.0425 to find the value of t.