Question

If you were to place $2,500 in a savings account that pays 5% interest compounded continuously, how much money will you have after 10 years? Assume you make no other deposits or withdrawals.
How would I go about finding this?

Answer 1

You would find what 5% of your account is the first year (which is $125), and add that to the account. Then go on to next year's, and find 5% of your new total, repeating the process.

Answer 2

Hmm, you sure Miss Snowfire?

Answer 3

Not sure if I missed anything, but I wouldn't doubt that fact (I am so clumsy >.>). Maybe I worded it wrong.

Answer 4

Hang on.. I'm looking through my notes for formulas.

Answer 5

But using the formula makes this much simpler, P(1+r/n)^nt

Answer 6

\(F = Pe^{rt} \)

Answer 7

Dang it, i was writing it out, but I think your formula is the right one, snowfire

Answer 8

When the interest is compounded continuously, you must use the formula with "e."

Answer 9

Yeah that's what the problem was, I hate e with a passion.

Answer 10

Sorry, yea, it's with Pert

Answer 11

But yeah, P is the starting balance (which is 2500), r is the interest rate as a decimal, and t is the time in years.

Answer 12

You can use the formula with n, as shown above, but you need to take the limit as n approaches infinity. The formula with "e" in it already does that for you.

Answer 13

Because e is magic, don't question its authority.

Answer 14

What do those values in the equation mean tho o.o
F = Pe^rt

Answer 15

Sham, pay attention

Answer 16

Snowfire said ir already xD

Answer 17

*it

Answer 18

F = Future value
P = present value
r = annual interest rate written as a decimal
t = number of years

\(\large F = Pe^{rt} \)

\(\large F = 2500e^{0.05 \times 10} \)

\( \large F = 2500e^{0.5} \)

Answer 19

So, now I just evaluate that.
F = 2500(2.71)^0.5
?

Answer 20

yes

Answer 21

Plug the 2500e^0.05*10 in your calculator.

Answer 22

4121.8

Answer 23

That's right.

Answer 24

correct

Answer 25

thank you all :D