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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 [#permalink] New post 07 Dec 2012, 02:29
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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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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] New post 07 Dec 2012, 02:35
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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:
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on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
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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] New post 25 Dec 2012, 15:52
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] New post 10 Jun 2013, 04:09
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Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

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

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] New post 25 Jun 2013, 23:32
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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] New post 25 May 2014, 15:47
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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Re: Leona bought a 1-year, $10,000 certificate of deposit that [#permalink] New post 27 May 2014, 02:18
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] 27 May 2014, 02:18
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