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Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 07 Dec 2012, 02:29 3 This post received KUDOS 18 This post was BOOKMARKED 00:00 Difficulty: 15% (low) Question Stats: 76% (02:06) correct 24% (01:24) wrong based on 1131 sessions ### HideShow timer Statistics Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 35909 Followers: 6846 Kudos [?]: 89983 [6] , given: 10396 Re: Leona bought a 1-year,$10,000 certificate of deposit that [#permalink]

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07 Dec 2012, 02:35
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Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? (A)$10,464
(B) $864 (C)$ 816
(D) $800 (E)$ 480

Approach #1:
8 percent compounded semiannually --> 4% in 6 moths.

For the first 6 moths interest was 4% of $10,000, so$400;
For the next 6 moths interest was 4% of $10,000, plus 4% earned on previous interest of$400, so $400+$16=$416; Total interest for 1 year was$400+$416=$816.

Approach #2:
If the interest were compounded annually instead of semiannually then in a year the interest would be 8% of $10,000, so$800. Now, since the interest is compounded semiannually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $800, only answer choice C fits. Answer: C. Similar questions to practice: john-deposited-10-000-to-open-a-new-savings-account-that-135825.html on-the-first-of-the-year-james-invested-x-dollars-at-128825.html marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html jolene-entered-an-18-month-investment-contract-that-127308.html alex-deposited-x-dollars-into-a-new-account-126459.html michelle-deposited-a-certain-sum-of-money-in-a-savings-138273.html Theory: math-number-theory-percents-91708.html Hope it helps. _________________ Manager Joined: 11 Aug 2012 Posts: 128 Schools: HBS '16, Stanford '16 Followers: 1 Kudos [?]: 97 [0], given: 16 Re: Leona bought a 1-year,$10,000 certificate of deposit that [#permalink]

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25 Dec 2012, 15:52
Bunuel, are the interest questions in the real GMAT as easy as this one?
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10 Jun 2013, 04:43
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The equation for compound interest is:
$$P_t = P_0(1+\frac{i}{n})^{nt}$$
$$P_t$$ is the Principle at time t
$$P_0$$ is the Principle at time 0
$$i$$ is the Interest Rate
$$n$$ is the Number of compounding periods
$$t$$ is the Number of years the investment earns interest

Plug in the numbers:
$$P_t = 10,000(1+\frac{.08}{2})^{2*1}$$

$$P_t = 10,000(1+\frac{8}{200})^{2}$$

$$P_t = 10,000(\frac{200}{200}+\frac{8}{200})^{2}$$

$$P_t = 10,000(\frac{208}{200})^{2}$$

$$P_t = 10,000(\frac{104}{100})^{2}$$

$$P_t = 10,000(\frac{10,816}{10,000})$$

$$P_t = 10,816$$

$$P_t - P_0= 10,816 - 10,000 = 816$$

Definitely a more difficult solution, but I know some people really like formulas.
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25 May 2014, 15:47
Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? (A)$10,464
(B) $864 (C)$ 816
(D) $800 (E)$ 480

I did it this way. I find it to be easy way for compound interest questions so maybe it will help someone.

annual interest 8%. semiannual = 4% (8/2) how many times 4%? 2 times

10 000x104/100x104/100=104x104=10 816

10 816-10 000=816
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15 Nov 2014, 04:35
I used the simple interest formula. which should give you 800 and slightly above that should give you the compound interest answer. therefore C

i think this is the best way to save time.
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23 Nov 2015, 13:34
the interest is (1 + 0.08/2)²
or 1,04*1,04 = 1,0816 or 8,16%

If compounded annualy : (1 + 0,08) or 8%
Compounded quaterly : (1 + 0,08/4)^4 or, 1,02^4 = 8,24%

The shorter the compound period, the higher the interest payment.
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 07 Jun 2016, 09:55 Walkabout wrote: Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 We use the compound interest equation: Future Value = (Present Value)(1 + r/n)^nt where r is the annual interest rate, n is the number of compounding periods per year and t is the amount of time (in years) until maturity. So we know: Present Value = 10,000 r = 8% = 0.08 n = 2 t = 1 So we have: FV = 10,000(1+0.08/2)^(2)(1) FV = 10,000(1+0.04)^2 FV = 10,000(1.04)(1.04) FV = 10,000(1.0816) =$10,816

Thus, the amount of interest earned is $10,816 –$10,000 = $816. We could have also looked at this problem a bit more conceptually. We know that when an investment has a rate of 8% ANNUAL interest and it compounds SEMI-ANNUALLY (twice a year), the investment earns 4% interest every SIX MONTHS. So in this case we know: Interest earned for the first six months = 0.04 x$10,000 = $400 Her investment is now worth ($400 + $10,000) =$10,400

Interest earned for the next six months = 0.04 x $10,400 =$416

Thus, the total interest earned = $400 +$416 = $816 Answer is C _________________ Jeffrey Miller Scott Woodbury-Stewart Founder and CEO Manager Joined: 21 Sep 2015 Posts: 85 Location: India GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41 Followers: 1 Kudos [?]: 54 [0], given: 322 Leona bought a 1-year,$10,000 certificate of deposit that [#permalink]

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12 Jun 2016, 04:44
A = 10000 * ( 1 +8 / 200) ^2

= 10000* (1.04 )^2

=104 * 10

Therefore units place of answer should have 6

Ans: 816

ScottTargetTestPrep why would anyone want to multiply 1.04 * 1.04
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] ### Show Tags 12 Jun 2016, 08:00 Walkabout wrote: Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 Compound interest= P (1+r/100n)^n 10,000 (1+8/200)^2 10,000 * 104/100 *104/100 Units digit will be 6. Only option C has units digit of 6 _________________ I welcome critical analysis of my post!! That will help me reach 700+ Re: Leona bought a 1-year,$10,000 certificate of deposit that   [#permalink] 12 Jun 2016, 08:00
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