Compound Interest

[cruz52]

How long will it take money to double if it is invested at 8% compound semiannually?


I know you have to use the formula 2p = A = P(1+ i)^mt

I did the steps 2(1 + .08/2)^2t

Than 2 = (1.04) ^2t

ln2 = 2tln(1.04) = t = ln/2ln(1.04) ... Every time I solve it out I get a decimal answer can anyone tell me what I am doing wrong?

 

[Deleted member 4993]

How long will it take money to double if it is invested at 8% compound semiannually?


I know you have to use the formula 2p = A = P(1+ i)^mt

I did the steps 2(1 + .08/2)^2t

Than 2 = (1.04) ^2t

ln2 = 2tln(1.04) = t = ln/2ln(1.04) ... Every time I solve it out I get a decimal answer can anyone tell me what I am doing wrong?

$\displaystyle 2*P \ = \ P*(1 + \frac{0.08}{2})^{2*t}$

$\displaystyle 2 \ = \ (1 + 0.04)^{2*t}$

$\displaystyle ln(2) \ = \ 2*t * ln(1 + 0.04)$

$\displaystyle t \ = \ \frac{ln(2)}{2*ln(1.04)}$

You are here without any troble

$\displaystyle t \ = \ \frac{0.693147181}{2 \ * \ 0.039220713}$

$\displaystyle t \ = \ \frac{0.693147181}{0.078441426}$

$\displaystyle t \ = \ 8.836493843 \ years$

This is correct - because "rule of 72" tells you that the answer should be ~9 years

You must be making some "punching" error.....