Thread: Logarithmic Applications

I'm doing a compound interest problem and I wanted to know if I am doing it correctly. The problem is


How long will it take for $1,000 to grow to $5,000 at an interest rate of 3.5% if interest is compounded

a) quarterly

b) continuously

For part a) I used the formula A = P(1 + r/n)^nt

5,000 = 1,000( 1 + .035/4)^4t

5 = (1.00875)^4t

ln5 = 4t ln1.00875

ln5 / 4ln1.00875 = T

Did I do it correctly? Perhaps i'm not putting it into the graphing calculator correctly but I keep getting the wrong answer compared to the answer section of the book. If I did do it correctly, can someone let me know what is the correct way to punch that into the calculator? I have a a Ti-83 graphing calculator.

For part b) I used the continuous forumula of A = Pe^rt

5,000 = 1,000e^.035t

5 = e^.035t

ln5 = .035t

ln5 / .035 = t

Did I do that correctly?

Thanks for any help

Hello, Jonathan!

How long will it take for $1,000 to grow to $5,000
at an interest rate of 3.5% if interest is compounded

a) quarterly

b) continuously


For part a) I used the formula: .

Then: .

. .

You are probably entering it incorrectly on your calculator.
Here's one common error . . .


We want: .

We must enter: .
. . . . . . . . . . . . . . . . .
When we press , the display shows: .
. . It automatically supplies the left parenthesis.

After we have entered the , we must close the parentheses with


If we don't, we will have: .
. . which the calculator interprets as: .