If a security currently worth $12,800 will be worth $15,573.16 five 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 rate of interest is 4.00%

Explanation:

Principal (initial security worth)- $ 12,800

Final amount - $ 15,573.16

Time taken – 5 years

No additional deposition or withdrawal in between

∴ Rate of interest

This is the problem pertaining to compounding interest.

We know that for compound interest

Amount (A)= Principal(P)(1+R/100)ⁿ

Where R= rate of interest

N= time period

Thus, equation can be rearranged as  

A/P=(1+R/100)ⁿ

Substituting the values of A, P and n as $15,573.16, $12800 and 5 years respectively

15573.16/12800=(1+R/100)⁵

Solving the above equation we would get R as 4%

answer; bootstrapping is your answer;