Question

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

Answer 1

<<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

Answer 2

yes

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

Answer 3

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

Answer 4

Well, for once we all agree :)

Answer 5

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.

Answer 6

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