Question

Sum of $1000 was invested for 4 years, and the interest was compounded semiannually. If this sum amounted to $1389.08 in the given time, what was the interest rate? Please round your answer to two decimal places.

Answer 1

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%