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Jolene entered an 18-month investment contract that Updated on: 04 Jun 2021, 01:18
Originally posted by Chembeti on 09 Feb 2012, 06:56.
Last edited by Bunuel on 04 Jun 2021, 01:18, edited 1 time in total.
Edited the question.
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71% (02:24) correct 29% (02:49) wrong based on 2650 sessions

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Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

This is very simple problem,yet need to pay attention to words in the problem
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E
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Jolene entered an 18-month investment contract that 09 Feb 2012, 07:13
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Chembeti
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

This is very simple problem,yet need to pay attention to words in the problem
Show more

If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.

Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;

Total: 200+306+(~420)=~$926.

Answer: E.
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Jolene entered an 18-month investment contract that 12 Aug 2012, 23:56
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Chembeti
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

This is very simple problem,yet need to pay attention to words in the problem
Show more


Using Compound Interest Formula method:
When rate of interest is R1%, R2% and R3% for 1st yr, 2nd yr and 3rd yr respectively, then

\(Amount = Principal[(1+ \frac{R1}{100}) (1+ \frac{R2}{100}) (1+ \frac{R3}{100})]\)

Applying the same formula here in this problem:

\(Amount = 10000[(1+ \frac{2}{100}) (1+ \frac{3}{100}) (1+ \frac{4}{100})]\)

= \(10000 * \frac{102}{100} * \frac{103}{100} * \frac{104}{100}\)

= \(102 * 103 * \frac{104}{100}\)

= 926.24 = OPTION E [Ans]
General Discussion
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Jolene entered an 18-month investment contract that 23 Apr 2012, 00:08
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I think my confusion still remains about the wording of the question

How would it be different if we were told that

contract guarantees to pay 2 percent interest per annum at the end of 6 months vs 2% interest at the end of 6 months.

Thanks
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Jolene entered an 18-month investment contract that 23 Apr 2012, 00:23
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raviram80
I think my confusion still remains about the wording of the question

How would it be different if we were told that

contract guarantees to pay 2 percent interest per annum at the end of 6 months vs 2% interest at the end of 6 months.

Thanks
Show more

There is a difference between simple and compound interests.

For more check this: math-number-theory-percents-91708.html

Similar questions:
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marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
10-000-is-deposited-in-a-certain-account-that-pays-r-65464.html
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You can find other question here;
PS: search.php?search_id=tag&tag_id=191
DS; search.php?search_id=tag&tag_id=192

Hope it helps.
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Jolene entered an 18-month investment contract that 23 Apr 2012, 16:33
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Bunuel
Chembeti
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

This is very simple problem,yet need to pay attention to words in the problem

If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.

Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;

Total: 200+306+(~420)=~$926.

Answer: E.
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Great cancelling out technique! so simple, calculate simple interest first and strike out answers below that. Great trick for if I am low on time. Thanks.
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Jolene entered an 18-month investment contract that 13 Apr 2014, 07:43
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Y the interest is not calculated as:

For first 6 months: [10,000*2*(6/12)]/100 =100
For next 6 months: [10100*3*(6/12)]/100 = 151.5
For next 6 months : [100251.5*4*(6/12)]/100 = 205.03

Adding the 3 interests= 456.53

What is wrong with using Simple Interest = P*R*T/100 formula??

Please explain!!


Thanks,
Shreya
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Jolene entered an 18-month investment contract that 22 Apr 2014, 03:27
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SHREYADUBEY
Y the interest is not calculated as:

For first 6 months: [10,000*2*(6/12)]/100 =100
For next 6 months: [10100*3*(6/12)]/100 = 151.5
For next 6 months : [100251.5*4*(6/12)]/100 = 205.03

Adding the 3 interests= 456.53

What is wrong with using Simple Interest = P*R*T/100 formula??

Please explain!!

Thanks,
Shreya
Show more

The problem states only the interest given; we have to calculate as it is

You are calculating using the PCPA concept (Per Cent Per Annum)

So, no need of that 6/12 or 4/12 multiplication.

For first 6 months: \(10,000* \frac{2}{100} = 200\)

For next 6 months: \(10200 * \frac{3}{100} = 306\)

For next 6 months: \(10506 * \frac{4}{100} = 420.24\)

Total Interest = 200 + 306 + 420.24

= 926.24

Answer = E
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Jolene entered an 18-month investment contract that 02 May 2014, 08:01
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Bunuel
Chembeti
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

This is very simple problem,yet need to pay attention to words in the problem

If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.

Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;

Total: 200+306+(~420)=~$926.

Answer: E.
Show more


Hi Bunnel, you are taking 9% simple interest annually on $10000, which you got $900 , but it should be 18 months to calculate interest of 9% on 10000


so SI = 10000 * 9 * 18 / 100 * 12
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Jolene entered an 18-month investment contract that 02 May 2014, 10:29
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Bunuel
Chembeti
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

This is very simple problem,yet need to pay attention to words in the problem

If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.

Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;

Total: 200+306+(~420)=~$926.

Answer: E.


Hi Bunnel, you are taking 9% simple interest annually on $10000, which you got $900 , but it should be 18 months to calculate interest of 9% on 10000


so SI = 10000 * 9 * 18 / 100 * 12
Show more

What I'm saying is that IF the interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000 in 18 months, which is $900.
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Jolene entered an 18-month investment contract that 24 Sep 2014, 06:58
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My first approach after reading the problem was: SI=P*R*T and that really complicated things for me.It was then when I started looking for an explanation to understand the language of the problem. During the search I came across a post, which really helped me to identify the issue in my approach. So thought of sharing it with fraternity.
Hope this help.

Lets suppose, I tell my friend to give me 100$,which I would return to him in 6-months, with 10% interest.
After 6-months how much I would be paying him?
100*(10/100)=110$.[I didn't use the time here.]
Now we can use the same approach to calculate the amount (P+I) over a period of time (6,12 & 18 months).
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Jolene entered an 18-month investment contract that 15 Dec 2017, 11:53
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Chembeti
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24
Show more

After 6 months, Jolene has 10,000 x 1.02 = 10,200 dollars.

After 12 months, Jolene has 10,200 x 1.03 = 10,506 dollars.

After 18 months, Jolene has 10,506 x 1.04 = 10,926.24 dollars.

Thus, the total interest made was 926.24 dollars.

Answer: E
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Jolene entered an 18-month investment contract that 03 Feb 2018, 16:50
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Hi All,

This question is really just about staying organized and doing the calculations one 'step' at a time.

Given the interest payments at 6 months, 12 months and 18 months, the first bit of interest on the $10,000 would be...

6 months: $10,000 + (.02)(10,000) = $10,200
Interest = $200

At the 12 month mark, the interest would be on $10,200 though...

12 months: $10,200 + (.03)(10,200) = $10,506
Interest = $306

At the 18 month mark, the interest would be on $10,506...

18 months: $10,506 + (.04)(10,506) = about $10,926
Interest = about $420

The question asks for the TOTAL interest earned. We can either add up the 3 interest payments OR since we know the final TOTAL, we can subtract $10,000 to determine the interest.

Final Answer:
Show Spoiler
E

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Hi All,

This question is really just about staying organized and doing the calculations one 'step' at a time.

Given the interest payments at 6 months, 12 months and 18 months, the first bit of interest on the $10,000 would be...

6 months: $10,000 + (.02)(10,000) = $10,200
Interest = $200

At the 12 month mark, the interest would be on $10,200 though...

12 months: $10,200 + (.03)(10,200) = $10,506
Interest = $306

At the 18 month mark, the interest would be on $10,506...

18 months: $10,506 + (.04)(10,506) = about $10,926
Interest = about $420

The question asks for the TOTAL interest earned. We can either add up the 3 interest payments OR since we know the final TOTAL, we can subtract $10,000 to determine the interest.

Final Answer:
Show Spoiler
E

GMAT assassins aren't born, they're made,
Rich
Show more


what I'm not getting is why you guys are using 2% as 2% . shouldn't it be 1% because the interest is given in only 6 months ? and with this logic the 4% interest should also be multiplied with 1.5 ?

what am I missing here ? please explain

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Jolene entered an 18-month investment contract that 26 Aug 2019, 13:18
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Hi All,

This question is really just about staying organized and doing the calculations one 'step' at a time.

Given the interest payments at 6 months, 12 months and 18 months, the first bit of interest on the $10,000 would be...

6 months: $10,000 + (.02)(10,000) = $10,200
Interest = $200

At the 12 month mark, the interest would be on $10,200 though...

12 months: $10,200 + (.03)(10,200) = $10,506
Interest = $306

At the 18 month mark, the interest would be on $10,506...

18 months: $10,506 + (.04)(10,506) = about $10,926
Interest = about $420

The question asks for the TOTAL interest earned. We can either add up the 3 interest payments OR since we know the final TOTAL, we can subtract $10,000 to determine the interest.

Final Answer:
Show Spoiler
E

GMAT assassins aren't born, they're made,
Rich


what I'm not getting is why you guys are using 2% as 2% . shouldn't it be 1% because the interest is given in only 6 months ? and with this logic the 4% interest should also be multiplied with 1.5 ?

what am I missing here ? please explain

Posted from my mobile device
Show more

Hi jackfr2,

If a question gives you an ANNUAL interest rate (meaning the rate that would occur if the calculation was done at the end of 1 year), but then asks you to calculate MORE than 1 time a year, then you divide the interest rate by the number of 'periods' in that year. For example, a 10% annual interest rate that's calculated every 6 months would be done in two '5% pieces" (one at the 6-month mark and one at that 12-month mark).

This question does NOT provide that type of information though. It tells us exactly what to calculate at each point in the timeline, so no adjustments to the calculation are needed.

GMAT assassins aren't born, they're made,
Rich
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Jolene entered an 18-month investment contract that 19 Feb 2021, 08:46
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In the question it is mentioned that -" If each interest payment is reinvested in the contract",how do we know whether this question comes under Compound interest or simple interest?
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Hi ImChasmish,

You'll likely see just one question that involves Interest Rates on Test Day - and those types of questions typically involve one or both of the standard Interest Rate formulas (Simple Interest and/or Compound Interest). This particular prompt does not involve either of those formulas though - and you know that because the prompt specifically states when and how the interest-calculations are to be done (re: every 6 months; 2% at the 6-month mark, 3% at the 12-month mark and 4% at the 18-month mark).

You can actually work through the 'math' in a number of different ways (depending on your preference for fractions or decimals), but it's essentially a series of small step-by-step calculations - and doesn't involve either of the standard Interest Rate formulas that you're asking about.

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Jolene entered an 18-month investment contract that 27 Apr 2021, 22:46
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Bunuel , please clarify.

Should we treat percent rate as "percent per annum" only if it is explicitly stated in the stem "percent per annum"? This problem confused me at first as I started calculation with the assumption that "2 percent interest at the end of 6 months" stands for 2 percent annual rate, thus making 1% for 6 month period and so on.

Thanks
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Jolene entered an 18-month investment contract that 03 Jun 2021, 21:03
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msu6800
Bunuel , please clarify.

Should we treat percent rate as "percent per annum" only if it is explicitly stated in the stem "percent per annum"? This problem confused me at first as I started calculation with the assumption that "2 percent interest at the end of 6 months" stands for 2 percent annual rate, thus making 1% for 6 month period and so on.

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Yup, I think only when the question states per annum is the rate per annum.
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Nikhil30
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Jolene entered an 18-month investment contract that 13 Jul 2021, 00:25
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raviram80
I think my confusion still remains about the wording of the question

How would it be different if we were told that

contract guarantees to pay 2 percent interest per annum at the end of 6 months vs 2% interest at the end of 6 months.

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if the interest is reinvested in the main principal that will be your compound interest. in the question its clearly mention the Amount is reinvested hence compound interest.
hope its clear .:)
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