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 = <span>$1389.08
P = </span><span>$1000
r = ?
n = 2 (it is semiannual)
x = 4
</span>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](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B%281%20%2B%20%20%5Cfrac%7Br%7D%7B2%7D%20%29%20%5E%7B8%7D%7D%20%20%20%3D%20%20%5Csqrt%5B8%5D%7B1.389%7D%20%20%5C%5C%20%0A1%20%2B%20%20%5Cfrac%7Br%7D%7B2%7D%20%3D1.04%20%5C%5C%20%0A%20%5Cfrac%7Br%7D%7B2%7D%20%3D%201.04-1%20%5C%5C%20%0A%20%5Cfrac%7Br%7D%7B2%7D%20%3D%200.04%20%5C%5C%20%0Ar%20%3D%202%2A0.04%20%3D0.08)
r = 0.08 = 8/100 = 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 = <span>$1389.08
P = </span><span>$1000
r = ?
n = 2 (it is semiannual)
x = 4
</span>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
r = 0.08 = 8/100 = 8%