Question

How long will it take for $2000 to double if it is invested at 6.25% interest compounded continuously? can some show me how to set this problem into this equation A=Pe^rt, please!

Answer 1

\[4000=2000e ^{.0625t}\]

Answer 2

\[2=e ^{.0625t}\]

Answer 3

\[\ln 2=.0625t(\ln e)\]

Answer 4

\[\frac{\ln2}{.0625}=t\]

Answer 5

\[11.09 yrs = t\]

Answer 6

can you please give me a crash course on what you did, Please...

Answer 7

Did you understand how the values were substituted into the equation?

Answer 8

no i didnt

Answer 9

A is the amount which was determined to be $4000 because the problem asked how long it would take a $2000 investment to double.

Answer 10

If $2000 doubles, it will then be $4000 would you agree?

Answer 11

So the problem is really asking "how long will it take $2000 to turn into $4000"

Answer 12

what does the e stand for?

Answer 13

The e is a frequently used mathematical constant. It doesn't stand for anything. It is sort of like pi. Just a commonly used constant. It is part of the formula just like pi is when you write

Answer 14

\[A=\pi r^2\]

Answer 15

You don't replace pi with anything and you don't replace e with anything.

Answer 16

can you help me figure out another problem but let me do it and maybe you can coach me.

Answer 17

It's numerical value (if you must know) is 2.718281828...

Answer 18

ok

Answer 19

Lay it on me.

Answer 20

What rate of interest compounded continuously is needed for an investment of $500 to grow to $900 in 10 years?

Answer 21

What is A?

Answer 22

900

Answer 23

What is P?

Answer 24

500

Answer 25

What is t?

Answer 26

10

Answer 27

What are you trying to find?

Answer 28

the rate of interest

Answer 29

Yes. r

Answer 30

So plug everything in.

Answer 31

900=500e^r10

Answer 32

\[900=500e ^{10r}\]

Answer 33

Divide both sides by 500

Answer 34

ok

Answer 35

In1.8=e^10r

Answer 36

\[1.8=e ^{10r}\]

Answer 37

Now when you take the natural log of both sides it should look like this:
\[\ln 1.8=\ln e ^{10r}\]

Answer 38

ok

Answer 39

Now bring the exponent down using the third law of logs and get this

Answer 40

\[\ln 1.8=10r \ln e\]

Answer 41

But of course ln e = 1 so we have:

Answer 42

\[\ln 1.8=10r\]

Answer 43

So just divide both sides by 10 and you are done

Answer 44

0.18=r

Answer 45

\[\frac{\ln 1.8}{10}=r=.05878=5.88 %\]

Answer 46

Did you take the natural log of 1.8 before you divided by 10?

Answer 47

no

Answer 48

Do you now how to do that?

Answer 49

no

Answer 50

You do understand that it says ln 1.8 divided by 10?

Answer 51

Do you have a scientific calculator?

Answer 52

yes

Answer 53

Can you find the ln button?

Answer 54

It's probably right next to the log button

Answer 55

yes i just pressed it and got the same as you did do i now dive that by 10

Answer 56

Yes

Answer 57

Now multiply by 100 to change it to percent.

Answer 58

got it you just answered my question!! thank you so much Mertsj

Answer 59

You're welcome and good luck. Isn't learning fun???!!!

Answer 60

yeah your the best!!!!!

Answer 61

Thanks.