Bunuel wrote:

How much interest will $2,000 earn at an annual rate of 8 percent in 1 year if the interest is compounded every 6 months?

(A) $160.00

(B) $163.20

(C) $249.73

(D) $332.80

(E) $2,163.20

Use answer choicesIf the compound interest rate compounded yearly instead of every six months, interest earned would equal the simple interest rate.*

That would be (2000)(.08) = $160 in interest.

But this rate gets paid twice in one year. So the amount earned must be a little more than $160.

I would go straight to answer B.

If you wanted to check:

(\(\frac{4}{100}\))($2000) = $80

(\(\frac{4}{100}\))($2080) = (4)(20.8) ~ 83$

Total 80 + ~ $83 = ~ $163

Answer B

Compound interest formula\(A= P(1 + \frac{r}{n})^{nt}\)

\(A = 2000(1.04)^2 = 2000(1.0816)=\)

$2,163.20

-2,000.00$163.20

Answer B

*

For just the first year, if compound interest rate compounds yearly, simple interest equals compound interest. Run the numbers with each formula. The result is identical: $160
_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"