If you deposit $1,000 into an account that pays 4% interest compounded continuously, how long will it take the account to grow to $2,000?

Question

If you deposit $1,000 into an account that pays 4% interest compounded continuously, how long will it 	take the account to grow to $2,000?

anonymous · Answer

is 19 months correct? if so is there a formula to figure this out?

anonymous · Answer

$$2=e^{.04t}$$ solve for $t$

anonymous · Answer

oh hell no, it is several years, approximately $\frac{72}{4}=18$ although it is probably a bit shorter

anonymous · Answer

oh okay, somebody told me 19 months

anonymous · Answer

can you help me work the problem out? @satellite73

anonymous · Answer

ok you are asked for how long it take your money to double from 1000 to 2000
for continuous compounding use 
$$P_0e^{rt}$$ in your case $r=.04,P_0=1000$ so solve 
$$2000=1000e^{.04t}$$ for $t$

anonymous · Answer

first step is divide by 1000 and get 
$$2=e^{.04t}$$ then in equivalent logarithmic form this is 
$$.04t=\ln(2)$$ so 
$$t=\frac{\ln(2)}{.04}$$

anonymous · Answer

18 was an over estimate i got from the rule of 72 real answer is a bit over 17 http://www.wolframalpha.com/input/?i=ln%282%29%2F.04

anonymous · Answer

you have helped me so much with this, thank you thank you!!