Question

how long would it take an investment of $500 to double at a rate of 5.5% compounded quarterly

Answer 1

\[i currently have 1/2(1+(0.055/4))^4xT\]

Answer 2

\[\left(\begin{matrix}1 \\ 2\end{matrix}\right)(1+ \frac{ 0.055 }{ 4 })^{4timesT}\]

Answer 3

solve
$$
\Large 2\cdot 500 = 500(1+\frac{0.055}{4})^{4t}

$$

Answer 4

haha latex >.< u got it
for space type ~

Answer 5

@perl ya thats how i got this equation i just dont know where to go from here.

Answer 6

i need to solve for T

Answer 7

the 1/2 would be on the other side of the equal sign wouldn't it?

Answer 8

@perl 1/2 or 2 on the left side?

Answer 9

woops, im thinking half-life

Answer 10

$$
\Large{
2\cdot 500 = 500(1+\frac{0.055}{4})^{4t}
\\ \iff \\
2= (1+\frac{0.055}{4})^{4t}



}
$$

Answer 11

better

Answer 12

ok now where from their?

Answer 13

$$
\Large{
2\cdot 500 = 500(1+\frac{0.055}{4})^{4t}
\\ \iff \\
2= (1+\frac{0.055}{4})^{4t}
\\ \iff \\
\ln 2= \ln (1+\frac{0.055}{4})^{4t}
\\ \iff \\
\ln 2= 4t \cdot \ln (1+\frac{0.055}{4})



}
$$

Answer 14

how do i get rid of ln? do they just cancel?

Answer 15

you can't remove ln, but you can solve for t

Answer 16

how so?

Answer 17

$$
\Large{
2\cdot 500 = 500(1+\frac{0.055}{4})^{4t}
\\ \iff \\
2= (1+\frac{0.055}{4})^{4t}
\\ \iff \\
\ln 2= \ln (1+\frac{0.055}{4})^{4t}
\\ \iff \\
\ln 2= 4t \cdot \ln (1+\frac{0.055}{4})

\\ \iff \\
\frac{\ln 2}{\ln (1+\frac{0.055}{4}) }= 4t


}
$$

Answer 18

oh! alright i think i got it

Answer 19

one sec

Answer 20

12.689?

Answer 21

@perl

Answer 22

\(\Large \dfrac{\ln 2}{4\ln (1+\frac{0.055}{4}) }= t \)

\(t = 12.689\)

Answer 23

You are correct.

Answer 24

yes

Answer 25

sweet thanks a ton!