# Having trouble

• Mar 15th 2008, 12:56 PM
Reward
Having trouble
1)An old coin was worth 50 cents originally and has been growing exponentially in value by 15% every year. Predict the coin's value after 3.5 years

2) Two investments are made. In one, $2500 is invested at 5% compounded annually. In other,$2000 is invested at 6% compounded annually. When will the investments have the same value?
• Mar 15th 2008, 01:05 PM
galactus
#1:

Since the coin increases $0.15/yr, then after the first year it is worth$0.575.

$0.575=0.50e^{k}$

$k=ln(1.15)$

$V=0.50e^{ln(1.15)t}$
• Mar 15th 2008, 01:26 PM
TheEmptySet
Using the forumula $P=P_0(1+\frac{r}{n})^{nt}$

we get the two equations

$P=2500(1.05)^{t}$ and

$P=2000(1.06)^{t}$

using substitution we get the equation

$2500(1.05)^{t}=2000(1.06)^t$

$(1.05)^t=\frac{4}{5}(1.06)^t$ taking ln of both sides

$ln(1.05)^t=ln(\frac{4}{5}(1.06)^t)$ using log properties

$tln(1.05)=ln(4/5)+tln(1.06)$ isolating t

$t(ln(1.05)-ln(1.06))=ln(4/5)$

$t=\frac{ln(0.8)}{(ln(1.05)-ln(1.06))}$