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Leona bought a 1-year, $10,000 certificate of deposit that

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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
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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


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.

Answer: C.

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
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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.
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 25 Dec 2012, 16:52
Bunuel, are the interest questions in the real GMAT as easy as this one?

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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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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:
\(P_t = 10,000(1+\frac{.08}{2})^{2*1}\)

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

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

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

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

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

\(P_t = 10,816\)

\(P_t - P_0= 10,816 - 10,000 = 816\)

Answer is C

Definitely a more difficult solution, but I know some people really like formulas.

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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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This problem can be solved using formula. However, the calculation in formula is difficult = 10,000(208/200)^2.

The main motive of GMAT behind Compound interest problem is to consume your time so that you waste your precious time in difficult calculations. We have to avoid that trap and use simple and fast calculations.

By definition Compound interest = S.I. + Interest on Interest

So here C.I. = 4% on 10,000 (6months) + 4% on 10,000(6months) + 4% on interest (last 6 months interest)

= 400 + 400 + 4*400/100
= 400 + 400 + 16 = 816
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 25 May 2014, 16:47
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



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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The amount increases in two steps : 4% in the first 6 months and again 4% in the second 6 months.

Such % change in two steps is knows as successive % change.

In case of successive % change, we can use the below formula to calculate the Net % change :

\(Net % change =\) \(A + B + \frac{AB}{100}\)

If there is % increase , we take the value as positive and for % decrease, we take that as negative.

In the final answer, positive number shows % increase and negative number shows % decrease.

Using the above formula , we get : net change = \(4 + 4 + \frac{4*4}{100}\) \(= 8 + .16 = 8.16 %\).

\(8.16 % of 10,000\) is 816. Hence the answer is 816.

This formula is applicable only in case of % change in two steps. In case % change takes place in 3 steps, we have to apply the formula for the first two first and then to the result and the third one.
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 15 Nov 2014, 05:35
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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Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 14 Apr 2015, 08:43
Is this approach correct?

Interest= (P*R*T)/100

For first 6 months, I = (10000*8*0.5)/100=400
Amount = P + I = 10400

For second 6 months, previous amount becomes the principal
I = (10400*8*0.5)/100= 416

So total interest = 400+416=816

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Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 23 Nov 2015, 14:34
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]

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New post 07 Jun 2016, 10:55
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
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Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 12 Jun 2016, 05:44
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 :lol:
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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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
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Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 27 Jun 2017, 08:36
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


\(A = 10000 ( 1 + \frac{8}{200})^2\)

Or, \(A = 10000*1.04^2\)

Or, \(A = 10816\)

So, Interest paid on this certificate at maturity is $ 816, answer must be (C)
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 27 Jun 2017, 12:57
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?

1. Premium for first 6 months: \(10,000 * \frac{8}{100}\) = \($ 800\)

As the interest is getting compounded semiannually, new principal will be = \($ 10,000 + $ 800\) = \($ 10,800\)

2. Premium for next 6 months: \(10,800 * \frac{80}{100}\)= \($816\)

Hence, Total Interest Paid = \($ 816\)

Hence, the Answer is C
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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink]

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New post 10 Sep 2017, 02:38
Compound interest formula is the best way to solve this problem.
But we can also use the simple interest formula: Amount*Rate*Time/100
= 10000*8*1/100
=800

The answer would be slightly more than 800 i.e. 816.
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Re: Leona bought a 1-year, $10,000 certificate of deposit that   [#permalink] 10 Sep 2017, 02:38
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