The answer is 8%
Compound interest formula is:
A = P(1 + r/n)ⁿˣ
A - the final amount
P - the initial amount
r - interest rate
n - number of compoundings per year
x - time period
We have:
A = $1389.08
P = $1000
r = ?
n = 2 (it is semiannual)
x = 4
A = P(1 + r/n)ⁿˣ
1389.08 = 1000(1 + r/2)²*⁴
1389.08 = 1000(1 + r/2)⁸
(1 + r/2)⁸ = 1389.08/1000
(1 + r/2)⁸ = 1.389
\(\sqrt[8]{(1 + \frac{r}{2} ) ^{8}} = \sqrt[8]{1.389} \\
1 + \frac{r}{2} =1.04 \\
\frac{r}{2} = 1.04-1 \\
\frac{r}{2} = 0.04 \\
r = 2*0.04 =0.08\)
r = 0.08 = 8/100 = 8%
