Find the compound interest earned. Round to the nearest cent. Do not use an interest table.
-$2,000 at 10% compounded semiannually for 3 years
A)$600.00
B)$662.00
C)$680.19
D)$1,543.12

Question

Quizplus · Accepted Answer

First, we need to find the interest rate per period. Since the interest is compounded semiannually, we divide the annual interest rate by 2:

$r = \frac{10\%}{2} = 0.05$

Next, we need to find the number of periods. Since the interest is compounded semiannually for 3 years, we have:

$n = 2 	imes 3 = 6$

Now, we can use the formula for compound interest:

$A = P\left(1 + \frac{r}{n}ight)^{nt}$

where:
- $A$ is the ending amount
- $P$ is the principal (starting amount)
- $r$ is the interest rate per period
- $n$ is the number of compounding periods per year
- $t$ is the number of years

Plugging in the given values, we get:

$A = 2000\left(1 + \frac{0.05}{2}ight)^{2	imes3} = 2000(1.025)^{6}$

Using a calculator, we get:

$A \approx 2680.19$

Therefore, the compound interest earned is:

$I = A - P = 2680.19 - 2000 = 680.19$

Rounding to the nearest cent, we get:

$I \approx 680.20$

Since the answer choices are rounded to the nearest cent, we choose:

C) $680.19$ We can use the compound interest formula A=P(1+r/n)^(nt) where:

A = the total amount with interest
P = the principal amount
r = the annual interest rate as a decimal
n = the number of times the interest is compounded per year
t = the time in years

Plugging in the values:

P = $2,000
r = 10% = 0.1
n = 2 (semiannually)
t = 3

A = 2000(1+0.1/2)^(2*3) = $2,680.19

So the compound interest earned is A - P = $680.19, which rounded to the nearest cent is $680.18. The closest choice is C, which is the correct answer.

Find the Compound Interest Earned