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# Already been answered a year ago, but found your working out confusing? if it takes 4 years for \$2000 to accumulate to \$4000, find the compound interest

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Hey guys.

Someone posted this same question on here about a year ago, and it was answered correctly (i checked my textbook and it was right). However I did not understand their working out? I've read through my textbook as well but I still don't understand how to do it!

Could you maybe break it down and try and explain it like you would for a preschooler? hahaha

The question:

if it takes 4 years for \$2000 to accumulate to \$4000, find the compound interest

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Let's work through it again....I assume you want the interest rate ??

Assuming yearly compounding, we're using

4000 = 2000(1 + r)^4      where r is the interest rate in decimal form

Divide both sides by 2000

4000/2000 =   2  =  (1 + r)^4

2  = (1 + r)^4       take the 4th root of both sides

2^(1/4)  = [ ( 1 + r)^4]  ^ (1/4)      the right side simplifies to   1 + r

2^(1/4)  = 1 + r      subtract 1 from both sides

2^(1/4)  - 1 =  r

1.1892  - 1  = r

.1892  = r  ≈ 18.92%   interest rate

CPhill  Feb 20, 2017