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Updated on: 06 Feb 2019, 01:02
4
35
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:27) correct 21% (01:47) wrong based on 1400 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

Originally posted by Walkabout on 07 Dec 2012, 02:29.
Last edited by Bunuel on 06 Feb 2019, 01:02, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Sep 2009
Posts: 53067
Re: Leona bought a 1-year, $10,000 certificate of deposit that paid intere [#permalink] ### Show Tags 07 Dec 2012, 02:35 13 19 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.

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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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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10 Jun 2013, 04:43
6
3
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.
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 53067

### Show Tags

25 Jun 2013, 23:32
4
2
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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### Show Tags

08 Jan 2015, 18:11
Hi All,

Interest rate questions are a relatively rare category on Test Day - you'll likely see just one question on the subject and it will involve one or both of the following formulas:

Simple Interest = Principal x (1 + RT)

Compound Interest = Principal x (1 + R)^T

...where R is the yearly interest rate and T is the number of years.

Normally, a question gives you the relevant information to work with, then asks you to perform the calculation. Sometimes there are "twists" though (eg. you're given the end result and have to "work backwards" to find the interest rate or principal) and in rare cases, you'll be asked to deal with a situation in which interest is compounded MORE than once per year.

The 'rule' for handling the Compound Interest Formula in this situation is pretty simple though:

For the number of times that you compound per year:
1) MULTIPLY T by that number
2) DIVIDE R by that number

For example, in this question we have $10,000 at 8% interest compounded SEMI-ANNUALLY (meaning twice per year) for 1 year. IF...we were just calculating ONCE per year, we'd have......$10,000 x (1 + .08)^1

For TWICE per year (which is what we have here)...............$10,000 x (1 + .04)^2 For FOUR times per year....................................................$10,000 x (1 + .02)^4

For EIGHT times per year...................................................$10,000 x (1 + .01)^8 Etc. As has been pointed out, the correct answer is . It's important to note the specific wording and numbers in these types of questions. It's common for one (or more) of the wrong answers to be the result of a DIFFERENT/INCORRECT calculation, so if you make a silly mistake, then you won't know that you are wrong. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Leona bought a 1-year, $10,000 certificate of deposit that paid intere [#permalink] ### Show Tags 08 Jan 2015, 21:28 3 xmagedo wrote: Lucy bought a 1-year,10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually. What was the total amount of interest paid on this certificate at maturity ? A. 10464 B. 864 C. 816 D. 800 E. 480 Is this formula right ?! I=a-p A= p(1+r/100)^n n= number of the year I applied this formula in the question and I keep getting 800, I dont know if it's right ? so pleas someone help me out Compound interest is different from simple interest in only one aspect - CI is earned on interest too. Annual Rate of interest = 8% Semi annual rate of interest = 4% (because interest is compounded semi annually) In the first half of the year, interest earned is 4% of 10000 =$400
In the second half of the year, $400 is earned plus interest is earned on the previous$400 i.e. 4% of 400 = $16 Total interest earned = 400 + 400 + 16 =$816
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### Show Tags

07 Jun 2016, 09:55
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

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Re: Leona bought a 1-year, $10,000 certificate of deposit that paid intere [#permalink] ### Show Tags 12 Jun 2016, 08:00 2 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+ Non-Human User Joined: 09 Sep 2013 Posts: 9894 Re: Leona bought a 1-year,$10,000 certificate of deposit that paid intere  [#permalink]

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06 Feb 2019, 01:01
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