# Continuous Compound Interest problem

• December 14th 2009, 11:51 AM
av8or91
Continuous Compound Interest problem
So I know this is the formula,
A
= Pe rt

To what final amount will an initial investment of $5,000 grow if the interest rate is 4% per year compounded continuously for 21 years? Write your answer rounded to the nearest cent. im getting a number of 7.994 but it doesnt seem right. • December 14th 2009, 12:02 PM e^(i*pi) Quote: Originally Posted by av8or91 So I know this is the formula, A = Pe rt To what final amount will an initial investment of$5,000 grow if the interest rate is 4% per year compounded continuously for 21 years? Write your answer rounded to the nearest cent.

im getting a number of 7.994 but it doesnt seem right.

Of course it's not right ;) as \$5000 > 7.994 and the problem implies that the amount increases

$P = 5000e^{21 \times 0.04} = \11,581.83$
• December 14th 2009, 12:13 PM
av8or91
I dont understand what im doing wrong. 5000e^(.04)(21) Then where do I proceed. P=.84ln5000e?
• December 14th 2009, 12:24 PM
pickslides
Quote:

Originally Posted by av8or91
I dont understand what im doing wrong.

You're doing nothing wrong,

evaluate this!

Quote:

Originally Posted by av8or91
5000e^(.04)(21)

• December 14th 2009, 12:32 PM
av8or91
Maybe thats my issue, im just evaluating it wrong. .84ln5000e does the equal .84ln13590? Then what I am doing is taking the natural log of 13590 mulitply by .84 but no thats not right.
• December 14th 2009, 12:46 PM
e^(i*pi)
Quote:

Originally Posted by av8or91
Maybe thats my issue, im just evaluating it wrong. .84ln5000e does the equal .84ln13590? Then what I am doing is taking the natural log of 13590 mulitply by .84 but no thats not right.

You don't need to use the natural log at all.

You're trying to find A given P, r and t. You can directly substitute the given values into the equation you gave in the OP to find a value for A
• December 14th 2009, 01:16 PM
av8or91
Maybe im a little stupid but thats why im here for help, (Headbang). Can you please show me how you are not using any natural logs and how you did it. Much appreciated. (Nod)
• December 14th 2009, 01:22 PM
pickslides
There are no logs in your original equation therefore consider

$A = Pe^{rt}$

inputing the information given

$A= 5000e^{0.04\times 21}$

$A = 5000e^{0.84}$

$A = 5000\times 2.316$

$A = 11,581.83$

that is all.
• December 14th 2009, 01:45 PM
av8or91
Ok Thanks. I see that now but when would you use ln
• December 14th 2009, 01:46 PM
pickslides
Quote:

Originally Posted by av8or91
Ok Thanks. I see that now but when would you use ln

In the problem you provided!?!
• December 14th 2009, 05:58 PM
DBA
In this problem you have all variables given (P, r and t)

In this example you would use ln:

How long will it take to double your investment if the interest would be 6% compounded continuousely?

A= P * e^rt

P = 1000
A = 2000
r = 0.06

2000 = 1000 * e^0.06*t
2 = e^0.06*t
ln2 = ln e^0.06*t --> ln e^x = x
ln2 = 0.06*t
t= ln2/0.06