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

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07 Dec 2012, 03:29

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C

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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?

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

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07 Dec 2012, 03:35

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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?

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.

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

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10 Jun 2013, 05:43

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

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

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26 Jun 2013, 00:32

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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)

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

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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?

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

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27 May 2014, 03:18

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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. _________________

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

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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?

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

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

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12 Jun 2016, 09:00

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?

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