Question

Which of the following is the interest on $6000 at 6% compounded semiannually for eight years?

Answer 1

Answer:

$3628.24

Step-by-step explanation:

we use the formula for accrued value (A) with compounded interest:

$A=P(1+\frac{r}{n})^{n*t}$

where A= accrued value (principal plus the accumulated  interest)

P = principal -> in our case $6000

r = annual interest rate (in decimal form) -> in our case 0.06

n = number of compoundings per year. In our case 2 (semiannually)

t = time in years -> in our case 8

$A=P(1+\frac{r}{n})^{n*t}\\A = 6000(1+\frac{0.06}{2})^{16}\\ A= 6000(1+0.03)^{16}\\A = 9628.24$

Since this is the value of principal plus accumulated interest, we subtract from it the principal ($6000) to get the value of just the interest:

$9628.24 - $6000 = $3628.24