How is "i" computed in the following problem?

Question

Calculate the compound interest rate. Compound interest is calculated based on the change in the cost index over the 4-yr period: 

 PV=FV(1+i)

4362=3684(1+i)^4

4362/3684=(1+i)^4

1.18404=(1+i)^4

i=4.31%

Answer 1

The first line is a formula for compound interest when the interest is not compounded continuously. Specifically,

A = the initial investment

i = the interest rate expressed as a decimal

n = the number of interest periods

B = the final sum of money

then B = A(1+i)ⁿ. If PV stands for principal value and FV stands for final value then you have those two things backwards.

The first step after that is just filling in what you know into the formula. The next step divides both sides by the principal value. The next step simplifies this. Finally the last step takes the 4th root of both sides, or another way of saying this is raises both sides to the 1/4 power. Because of exponent rules, that will cancel out the 4 on the right side of the equation. So in slightly more detail:

1.18404 = (1+i)⁴

1.18404^(1/4)=((1+i)⁴)^(1/4)

1.04314 = (1+i)

0.04314 = i

i = 4.31%