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22 Oct 2017, 06:13
00:00

Difficulty:

35% (medium)

Question Stats:

63% (00:53) correct 37% (01:21) wrong based on 76 sessions

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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

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22 Oct 2017, 13:57
1
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

If 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

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

*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" Intern Joined: 27 Sep 2017 Posts: 1 How much interest will$2,000 earn at an annual rate of 8 percent in  [#permalink]

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23 Oct 2017, 09:40
2000*(1+.08/2)^2=163.20
shortcut,
8% compunded half-yearly for 1 year ..>>so,8%/2=4%
now, use successive method for interest calculation>>(a+b+(a+b)/100).
4%+4%+(4%*4%)/100=8%+.16%=8.16%
>>2000*8.16%=163.20
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Joined: 09 Aug 2017
Posts: 62
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GMAT 1: 640 Q44 V33
GMAT 2: 630 Q47 V29
WE: Research (Investment Banking)
How much interest will $2,000 earn at an annual rate of 8 percent in [#permalink] ### Show Tags 25 Oct 2017, 13:15 8% compounded semiannually is really 4% compounded twice. -So I took 4% * 2,000 = 80. -Then I did 4% * 2000 + 4%*80 = 80+3.2=83.2 80+83.2=163.2, B. _________________ I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it. Also, I appreciate any kudos. How much interest will$2,000 earn at an annual rate of 8 percent in &nbs [#permalink] 25 Oct 2017, 13:15
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