SOLUTION: Can you help me with this question please? How many years will it take $5000 to grow to $8000 if the investment is at 6.5% and is compounded quarterly? I used the compound i

Algebra ->  Finance -> SOLUTION: Can you help me with this question please? How many years will it take $5000 to grow to $8000 if the investment is at 6.5% and is compounded quarterly? I used the compound i      Log On


   

Question 923482: Can you help me with this question please?
How many years will it take $5000 to grow to $8000 if the investment is at 6.5% and is compounded quarterly?
I used the compound interest formula
A=P(1+(r/n))^(nt)
and got the formula:
8000=5000(1+(.065/3))^3t
but I am not sure how to get the t alone...
could you divide both sides by 5000?
then it would be 8000/5000= (1+(.065/3))^3t
I am not sure...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
How many years will it take $5000 to grow to $8000 if the investment is at 6.5% and is compounded quarterly?


A=P%281%2Br%2Fn%29%5E%28nt%29


8000=5000%281%2B0.065%2F4%29%5E%284%2At%29


8000=5000%281%2B0.01625%29%5E%284%2At%29


8000=5000%281.01625%29%5E%284%2At%29


8000%2F5000=%281.01625%29%5E%284%2At%29


1.6=%281.01625%29%5E%284%2At%29


log%28%281.6%29%29=log%28%28%281.01625%29%5E%284%2At%29%29%29 Apply logs to both sides


log%28%281.6%29%29=%284%2At%29%2Alog%28%281.01625%29%29


log%28%281.6%29%29=t%2A4%2Alog%28%281.01625%29%29


log%28%281.6%29%29%2F%284%2Alog%28%281.01625%29%29%29=t


t+=+log%28%281.6%29%29%2F%284%2Alog%28%281.01625%29%29%29


t+=+7.28941768282519 Use a calculator. Type in "log(1.6)/(4*log(1.01625))" 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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