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Jerry purchased a 1-year $5,000 bond that paid an annual

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Jerry purchased a 1-year $5,000 bond that paid an annual  [#permalink]

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New post 19 Jun 2011, 07:55
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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: Interest Problem  [#permalink]

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New post 19 Jun 2011, 09:00
I doubt if it is a 700 level question.Anyways A=P(1+r/q)nq .Here q is no of times interest is compounded in a yr so it is = 2. Amount comes out to be 5202 .Hence interest is 5202-5000=202. >>D
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Re: Jerry purchased a 1-year $5,000 bond that paid an annual  [#permalink]

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New post 12 Sep 2017, 04:09
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

Answer: D
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Jerry purchased a 1-year $5,000 bond that paid an annual  [#permalink]

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New post 13 Sep 2017, 11:14
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
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Re: Jerry purchased a 1-year $5,000 bond that paid an annual  [#permalink]

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New post 13 Sep 2017, 12:37
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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?
TOTAL interest = $5202 - $5000 = $202

Answer:

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Re: Jerry purchased a 1-year $5,000 bond that paid an annual  [#permalink]

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New post 14 Sep 2017, 05:57
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]

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New post 09 Oct 2018, 08:18
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)
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Re: Jerry purchased a 1-year $5,000 bond that paid an annual  [#permalink]

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New post 12 Oct 2018, 07:52
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.

Answer: D
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Re: Jerry purchased a 1-year $5,000 bond that paid an annual   [#permalink] 12 Oct 2018, 07:52
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