Question 923482
How many years will it take $5000 to grow to $8000 if the investment is at 6.5% and is compounded quarterly? 



{{{A=P(1+r/n)^(nt)}}}



{{{8000=5000(1+0.065/4)^(4*t)}}}



{{{8000=5000(1+0.01625)^(4*t)}}}



{{{8000=5000(1.01625)^(4*t)}}}



{{{8000/5000=(1.01625)^(4*t)}}}



{{{1.6=(1.01625)^(4*t)}}}



{{{log((1.6))=log(((1.01625)^(4*t)))}}} Apply logs to both sides



{{{log((1.6))=(4*t)*log((1.01625))}}}



{{{log((1.6))=t*4*log((1.01625))}}}



{{{log((1.6))/(4*log((1.01625)))=t}}}



{{{t = log((1.6))/(4*log((1.01625)))}}}



{{{t = 7.28941768282519}}} Use a calculator. Type in "<font color="blue">log(1.6)/(4*log(1.01625))</font>" without quotes



It will take approximately 7.28941768282519 years



Round this up to the nearest whole year to get 8 years.


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Let me know if that helps or not. Thanks.


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