## Rugtugba 2 years ago If you deposit \$1,000 in an account that pays 6% annual interest compounded continuously, what will the balance be after five years?

1. Kuoministers

any idea how to formulate a equation for that?

2. Rugtugba

no :/ cantremember

3. Mertsj

I believe the formula is \[A = Pe ^{rt}\]

4. Kuoministers

Conpound interest can be calculated using the formula

5. Kuoministers

6. Kuoministers

P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal) t = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. n = number of times the interest is compounded per year

7. Kuoministers

remember your interest compounds annually(every year)

8. Mertsj

@Kuoministers That is indeed the formula for compound interest where you have a finite number of compounding periods. However, in this problem, the interest is compounded continuously. So the formula I posted is the one to use and I am afraid you are confusing the asker. Why don't you google "interest formula compounded continuously"?

9. MariaB2014

@Mertsj is right .

10. Kuoministers

ah yes my bad @mertsj :)

11. Kuoministers

but it still would work if you used the formula that i had?

12. Mertsj

So Rugtugba, now that we have cleared the chatter, are you ready to continue?

13. Rugtugba

yes

14. Mertsj

@Kuoministers What would you use for n?

15. Kuoministers

1 since its compounded yearly

16. Mertsj

Plug into the formula. The initial amount A is Ok. Let me deal with the cat first.

17. Rugtugba

lol

18. Mertsj

@Kuoministers So compounded continuously means annually? I thought compounded annually meant compounded annually. Silly me!!

19. Mertsj

Good luck, Rugtugba. We have way too many cooks in this kitchen.

20. tkhunny

@Kuoministers the continuous forumla is the limiting form of the finite form you have posted. Your calculus will have to be up to speed to prove it. You can explore it on your own by calculating the finite formula multiple times, each with an increasing value of n.

21. Rugtugba

its alright guys i found it its 1349.60 thanks anyways