SOLUTION: Jimmy invests ​$20000 in an account that pays 5.14% compounded quarterly. How long​ (in years and​ months) will it take for his investment to reach ​$24000​?

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Question 1139100: Jimmy invests ​$20000 in an account that pays 5.14% compounded quarterly. How long​ (in years and​ months) will it take for his investment to reach ​$24000​?
Answer by ikleyn(52919) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "n" be the number of quarter periods.


24000 = 20000%2A%281%2B0.0514%2F4%29%5En,


24000%2F20000 = %281%2B0.0514%2F4%29%5En


1.2 = %281%2B0.0514%2F4%29%5En


log(1.2) = n%2Alog%28%281%2B0.0514%2F4%29%29


n = log%28%281.2%29%29%2Flog%28%281%2B0.0514%2F4%29%29 = 14.28 quarter periods.



ANSWER. 15 quarter periods are enough.


CHECK.  20000%2A%281%2B0.0514%2F4%29%5E15 = 24221.83 dollars.

Solved.