Question 966057
<font color="blue">How long will it take for the value of this investment to reach $11,500? Round your answer to two decimal places.</font>



Use logs to isolate the exponent.



{{{V(n) =2308.43(1.019)^n}}}



{{{11500 =2308.43(1.019)^n}}}



{{{11500/2308.43=(1.019)^n}}}



{{{4.9817408368=(1.019)^n}}}



{{{(1.019)^n = 4.9817408368}}}



{{{log(((1.019)^n)) = log((4.9817408368))}}}



{{{n*log((1.019)) = log((4.9817408368))}}}



{{{n = log((4.9817408368))/log((1.019))}}}



{{{n = 85.31507611}}}



{{{n = 85.32}}}



It will take roughly <font color="red">85.32 years</font>


Side note: the reason why it takes so long is because the interest rate is quite dismal. The interest rate of 1.9% is very very small compared to better investments out there.


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I'll let you do the second part. You simply plug in V(n) = 4600 (since 2,300*2 = 4,600) and solve for n using logs. The steps are similar to above because you'll also use logs to isolate n.


If you need help with the second part, then let me know.