Pre-calc - continual compounding interest

[doright]

Problem:

You put money in two banks. $2000 in bank A at an interest rate of 11%; $4000 in bank B at an interest rate of 6%.

How many years will it take for the deposits to be of equal value and what will that amount be?

My granddaughter is working on this problem in a college pre-calc class and I'm trying to help her because her tutor is unavailable. (It's been 40+ years since I did any of this, sorry.)

My thoughts were to use the future value formula on each side making them equal to one another and solving for 't'. Once you get 't', then, you can calculate the value. So...

Using FV=Pe^rt...

2000e^.11t=4000e^.06t

I don't even know if the approach is correct. I could be off my rocker and, of course, I can't figure out how to solve this equation I've created.

I was thinking to make the bases (2000 & 4000) the same and then just calculate using the exponents, but, I've forgotten how to do that... or if it's even possible or correct.

Any help would be sincerely appreciated and I'm sorry if this is in the wrong category. To me, it should be a financial category, but, since it's a pre-calc class I'm posting it here.

Thanks,
Sheryl

 

[Deleted member 4993]

Problem:

You put money in two banks. $2000 in bank A at an interest rate of 11%; $4000 in bank B at an interest rate of 6%.

How many years will it take for the deposits to be of equal value and what will that amount be?

My granddaughter is working on this problem in a college pre-calc class and I'm trying to help her because her tutor is unavailable. (It's been 40+ years since I did any of this, sorry.)

My thoughts were to use the future value formula on each side making them equal to one another and solving for 't'. Once you get 't', then, you can calculate the value. So...

Using FV=Pe^rt...

2000e^.11t=4000e^.06t

I don't even know if the approach is correct. I could be off my rocker and, of course, I can't figure out how to solve this equation I've created.

I was thinking to make the bases (2000 & 4000) the same and then just calculate using the exponents, but, I've forgotten how to do that... or if it's even possible or correct.

Any help would be sincerely appreciated and I'm sorry if this is in the wrong category. To me, it should be a financial category, but, since it's a pre-calc class I'm posting it here.

Thanks,
Sheryl

2000e^.11t=4000e^.06t

[e^.11t]/ [e^.06t] = 2

e^(.11-.06)t = 2

0.05t = ln(2) → t = 20 * ln(2) → t = 13.86294

 

[lookagain]

You put money in two banks. $2000 in bank A at an interest rate of 11%; $4000 in bank B at an interest rate of 6%.

How many years will it take for the deposits to be of equal value and what will that amount be?


Using FV=Pe^rt...

2000e^.11t=4000e^.06t

That equation should work.


You could divide each side by 2000 to get to:

e^.11t = 2e^.06t



That equation should work.


doright, realistically speaking, because it's been 40+ years since you have done this material,
I don't expect you to be able to follow the solution given to you by Subhotosh Khan above that
a student working with that material would follow with relative ease/understanding.

 

[doright]

2000e^.11t=4000e^.06t

[e^.11t]/ [e^.06t] = 2

e^(.11-.06)t = 2

0.05t = ln(2) → t = 20 * ln(2) → t = 13.86294

Thank you! I'm hoping she will understand this.

 

[doright]

You're right, Lookagain

That equation should work.


You could divide each side by 2000 to get to:

e^.11t = 2e^.06t



That equation should work.


doright, realistically speaking, because it's been 40+ years since you have done this material,
I don't expect you to be able to follow the solution given to you by Subhotosh Khan above that
a student working with that material would follow with relative ease/understanding.

Well, DUH... on dividing on both sides. I was making it WAY more complicated.

You're absolutely right, Lookagain. I'm beginning to think that I need to go back to middle school. Thank you!

 

[doright]

To all of y'all.....

Thank you all so much for your help. I'm sure you have better things to do than make a hero out of an old lady!! :lol:

Whatever you do, don't lose your math skills by not using them. In my 20's I would pull out my college math books and do proofs or solve random problems for fun. (To me, math was always just puzzle solving.) Then, the kiddies and life intervened.... 40+ years later I'm trying to remember the commutative property of addition!!

So, thank you for your service to mathkind and keep up the good work!

Sincerely,
Sheryl