# Interest Compounded Continuously

• Nov 8th 2009, 04:47 PM
fscc
Interest Compounded Continuously
Currently has $4679, but know he can get a loan at a lower interest rate if he can put down$5489. If he invests the $4679 in an account that earns 4.1% annually, compounded continuously, how long will it take him to accumulate the$5489?

Can anybody help me with working this problem.
• Nov 8th 2009, 04:57 PM
TKHunny
Once you've seen it, you will know.

$\displaystyle 4679 \cdot e^{t*0.041}\;=\;5489$

Solve for 't'.
• Nov 8th 2009, 04:58 PM
fscc
ok thank you for your help...ok still need help on solving it...mine aint working out right?!
• Nov 8th 2009, 08:39 PM
Bacterius
$\displaystyle 4679 \cdot e^{t \times 0.041}\;=\;5489$

$\displaystyle e^{t \times 0.041}\;=\; \frac{ 5489}{4679}$

$\displaystyle ln(e^{t \times 0.041})\;=\; ln(\frac{ 5489}{4679})$

$\displaystyle t \times 0.041\;=\; ln(\frac{ 5489}{4679})$

$\displaystyle t \;=\; \frac {ln(\frac{ 5489}{4679})}{0.041}$

$\displaystyle t \; \approx \; 3,89$ (2 d.p.)
• Nov 9th 2009, 01:31 PM
TKHunny
Quote:

Originally Posted by fscc
ok thank you for your help...ok still need help on solving it...mine aint working out right?!

(Worried) Not good. You should have prerequisites that include simple exponentials and logarithms before getting to this class. Have you been skipping around the curriculum?