Question

please help ;/
How long, to the nearest year, will it take me to become a millionaire if I invest $3000 at 12% interest compounded continuously? HINT [See Example 3.]

Answer 1

have you covered logarithms yet?

Answer 2

yes

Answer 3

but I'm having difficulty

Answer 4

i thought it was 96 yr but nothing

Answer 5

well, you're given the principal and the rate
you'd just need to solve for "t" in the continously compound formula

Answer 6

isn't it 12ln3000?

Answer 7

well... one sec

Answer 8

ok

Answer 9

\(\bf A=Pe^{rt}
\\ \quad \\
A=1,000,000\qquad P=3,000\qquad r=0.12
\\ \quad \\
1,000,000=3,000e^{0.12t}\implies \cfrac{1,000}{3}=e^{0.12t}
\\ \quad \\
ln\left(\frac{1,000}{3}\right)=0.12t\implies \cfrac{ln\left(\frac{1,000}{3}\right)=}{0.12}=t\)

Answer 10

i knew i was missing a number i completely forgot about 1000000

Answer 11

so you'll be a millionarie, but you'd be also about 70 years old too :P
minus inflation you'd have less buying power anyway

Answer 12

haha nice one! :) thank you for all your help i was stuck on it for an hour!

Answer 13

yw

Answer 14

one day i hope to know math as good as you it my weakest subject :/