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19 Jun 2011, 06:55
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Difficulty:

65% (hard)

Question Stats:

54% (01:30) correct 46% (01:50) wrong based on 186 sessions

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Jerry purchased a 1-year $5,000 bond that paid an annual interest rate of 4% compounded every six months. How much interest had this bond accrued at maturity? A.$5102
B. $408 C.$216
D. $202 E.$200
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Re: Jerry purchased a 1-year $5,000 bond that paid an annual [#permalink] ### Show Tags 13 Sep 2017, 11:37 2 Top Contributor 1 guygmat wrote: Jerry purchased a 1-year$5,000 bond that paid an annual interest rate of 4% compounded every six months. How much interest had this bond accrued at maturity?

A. $5102 B.$408
C. $216 D.$202
E. $200 The ANNUAL interest rate = 4% So, every 6 MONTHS, we get 2% interest. Since there are only 2 "compoundings," we can forgo the formula and do some quick mental calculations... INITIAL VALUE:$5000

AFTER 6 MONTHS: 2% of $5000 =$100 in interest
So, the value after 6 months = $5000 +$100 = $5100 AFTER 12 MONTHS: 2% of$5100 = $102 in interest So, the value after 12 months =$5100 + $102 =$5202

How much interest had this bond accrued at maturity?

### Show Tags

12 Sep 2017, 03:09
Here P = 5000
r=4%
time = 1 year
As the amount is compounded annually n = 2

Compound interest formula = $$A = p* (1+\frac{r}{n*100}) ^n^t$$
$$A = 5000* (1+\frac{4}{2*100}) ^(2*1)$$
A= 5202

So Interest earned = 5202 - 5000 = 202

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Jerry purchased a 1-year $5,000 bond that paid an annual [#permalink] ### Show Tags 13 Sep 2017, 10:14 guygmat wrote: Jerry purchased a 1-year$5,000 bond that paid an annual interest rate of 4% compounded every six months. How much interest had this bond accrued at maturity?

A. $5102 B.$408
C. $216 D.$202
E. $200 Estimate Without the compound interest formula (I use it, but with short periods and low interest rate, often you can estimate): Simple interest would yield .04 * 5,000 =$200 in one year

Compound interest at this low rate (halved and paid twice), after only one year, will be barely above that.

Answer D, $202 is barely above$200.

Stages

If unsure about Answer C ($216), run a quick "in stages" calculation. If interest is paid every 6 months, the 4 percent is split in half (two periods of six months in one year). After first six months, interest payment is$5,000 * 02 = $100 (add$100 to principal for next stage)

After next six months,
.02 * $5,100 =$102

Total interest paid: $202 ANSWER D _________________ Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date. Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has. -- Margaret Mead Director Joined: 02 Sep 2016 Posts: 629 Re: Jerry purchased a 1-year$5,000 bond that paid an annual  [#permalink]

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14 Sep 2017, 04:57
Simple interest= 5000*4*1/100= 200

So the answer would be a number that is slightly more than 200 i.e. 202.
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Re: Jerry purchased a 1-year $5,000 bond that paid an annual [#permalink] ### Show Tags 09 Oct 2018, 07:18 guygmat wrote: Jerry purchased a 1-year$5,000 bond that paid an annual interest rate of 4% compounded every six months. How much interest had this bond accrued at maturity?

A. $5102 B.$408
C. $216 D.$202
E. $200 $$5000( 1 + \frac{4}{200})^2 - 5000$$ $$= 5202 - 5000$$ $$= 202$$, Answer must be (D) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 9952 Location: United States (CA) Re: Jerry purchased a 1-year$5,000 bond that paid an annual  [#permalink]

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12 Oct 2018, 06:52
guygmat wrote:
Jerry purchased a 1-year $5,000 bond that paid an annual interest rate of 4% compounded every six months. How much interest had this bond accrued at maturity? A.$5102
B. $408 C.$216
D. $202 E.$200

Since the annual interest rate is 4%, we see that the bond earns 2% every half-year, or 6 months. Thus, for the first 6 months, the amount of interest earned was 0.02 x 5,000 = 100 dollars. Thus, the new principal at the end of the first 6 months was 5,000 + 100 = 5,100 dollars.

For the next 6 months, the amount of interest earned was 0.02 x 5100 = 102 dollars.

So total interest earned is 202 dollars.

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Re: Jerry purchased a 1-year $5,000 bond that paid an annual [#permalink] ### Show Tags 06 Jan 2020, 17:49 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Jerry purchased a 1-year$5,000 bond that paid an annual   [#permalink] 06 Jan 2020, 17:49
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