If a security currently worth $12,800 will be worth $16,843.93 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

The implied interest rate will be 4%

Explanation:

We need to check for the annual rate that generate the interest over the next seven years that makes $12,800 become $16,843.93:

We replace with our know values

12,800 x (1+rate)^7   = 16,843.93

16,843.93 /12,800    =  (1+rate)^7

sq7 (16,843.93/12,800) - 1 = rate

And know we find out the unknow value

rate = 0,03999994  =  0.04  = 4%

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