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Jolene entered an 18-month investment contract that

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Jolene entered an 18-month investment contract that [#permalink] New post 09 Feb 2012, 05:56
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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
[Reveal] Spoiler: OA

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Re: Simple Interest Calculation [#permalink] New post 09 Feb 2012, 06:13
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Chembeti wrote:
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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Simple Interest Question: MGMAT CAT Tests [#permalink] New post 22 Apr 2012, 21:10
Hi,

I saw this question in the exam and the solution looks like is not considering interest rates as per annum. So is it true that if per annum is not specified with the interest rates we dont need to put the time in calculation as a ratio of months/year.

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?



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Re: Simple Interest Question: MGMAT CAT Tests [#permalink] New post 22 Apr 2012, 21:14
Expert's post
raviram80 wrote:
Hi,

I saw this question in the exam and the solution looks like is not considering interest rates as per annum. So is it true that if per annum is not specified with the interest rates we dont need to put the time in calculation as a ratio of months/year.

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?



Thanks


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Re: Jolene entered an 18-month investment contract that [#permalink] New post 22 Apr 2012, 23:08
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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Re: Jolene entered an 18-month investment contract that [#permalink] New post 22 Apr 2012, 23:23
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raviram80 wrote:
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


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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PS: search.php?search_id=tag&tag_id=191
DS; search.php?search_id=tag&tag_id=192

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Re: Jolene entered an 18-month investment contract that [#permalink] New post 23 Apr 2012, 10:17
Thanks, I understand now.

This is the line which means compound interest


"If each interest payment is reinvested in the contract"
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Re: Jolene entered an 18-month investment contract that [#permalink] New post 23 Apr 2012, 10:32
raviram80 wrote:
Thanks, I understand now.

This is the line which means compound interest


"If each interest payment is reinvested in the contract"

This isn't really a compound interest. All that it says is that the interest received is used again in the contract. Nowhere in the statement is it explicitly or implicitly stated that its a compound interest and the answer too are pretty simple to derive if you don't lost in the dilemna of Simple and compounded interest.
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Re: Simple Interest Calculation [#permalink] New post 23 Apr 2012, 15:33
Bunuel wrote:
Chembeti wrote:
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.


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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Re: Simple Interest Calculation [#permalink] New post 23 Apr 2012, 15:34
Bunuel wrote:
Chembeti wrote:
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.


Great elimination method if I am low on time. Thanks!
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Re: Jolene entered an 18-month investment contract that [#permalink] New post 12 Aug 2012, 22:56
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Chembeti wrote:
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



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]
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Re: Jolene entered an 18-month investment contract that [#permalink] New post 14 Oct 2013, 08:01
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Re: Jolene entered an 18-month investment contract that [#permalink] New post 13 Apr 2014, 06:43
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,
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Re: Jolene entered an 18-month investment contract that [#permalink] New post 22 Apr 2014, 02:27
SHREYADUBEY wrote:
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


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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Re: Simple Interest Calculation [#permalink] New post 02 May 2014, 07:01
Bunuel wrote:
Chembeti wrote:
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
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Re: Simple Interest Calculation [#permalink] New post 02 May 2014, 09:29
Expert's post
riteshgmat wrote:
Bunuel wrote:
Chembeti wrote:
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


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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Jolene entered an 18-month investment contract that [#permalink] New post 08 Aug 2014, 02:40
Bunuel wrote:
Chembeti wrote:
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.



Bunuel, could you please confirm

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
Re: Jolene entered an 18-month investment contract that   [#permalink] 08 Aug 2014, 02:40
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