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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]

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New post 09 Feb 2012, 06:56
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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

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Re: Simple Interest Calculation  [#permalink]

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New post 09 Feb 2012, 07:13
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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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Re: Jolene entered an 18-month investment contract that  [#permalink]

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New post 12 Aug 2012, 23:56
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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]

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New post 23 Apr 2012, 00:08
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.

Thanks
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New post 23 Apr 2012, 00:23
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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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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Re: Jolene entered an 18-month investment contract that  [#permalink]

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New post 23 Apr 2012, 11:17
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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New post 23 Apr 2012, 11:32
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]

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New post 23 Apr 2012, 16:33
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]

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New post 23 Apr 2012, 16:34
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]

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New post 13 Apr 2014, 07:43
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,
Shreya
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Re: Jolene entered an 18-month investment contract that  [#permalink]

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New post 22 Apr 2014, 03:27
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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]

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New post 02 May 2014, 08:01
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]

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New post 02 May 2014, 10:29
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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Re: Jolene entered an 18-month investment contract that  [#permalink]

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New post 08 Aug 2014, 03:40
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

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Jolene entered an 18-month investment contract that  [#permalink]

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New post 22 Sep 2014, 23:46
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.



I got the entire concept except the fact that when Simple interest is calculated why is (n) time period NOT included in the calculation:

S.I. p*n*r = 10,000 * 9% * n (where n = 1.5 years)

Kindly clarify.
Thanks in advance
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Jolene entered an 18-month investment contract that  [#permalink]

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New post 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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Re: Jolene entered an 18-month investment contract that  [#permalink]

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New post 25 Sep 2014, 03:12
JarvisR wrote:
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).


So basically when or how does one figure that in a certain problem, it is best to avoid (n) while calculating Interest?
Its definitely not the 6,12,18 months timeline that can be ignored then how does one go about it?
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New post 29 Jul 2016, 02:44
I have a doubt!! why did you add $6 and $ 8 for the second and third interest rates?
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Jolene entered an 18-month investment contract that  [#permalink]

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New post Updated on: 25 Apr 2017, 06:22
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.

after first interest 3% is given to which amount.we dont see any clear wording here. why shold we not assume that it will be given for previous amount (10000)+10000 for reinvested +200 instead only 10000+200. plz clarify me

Originally posted by anik2000 on 25 Apr 2017, 06:10.
Last edited by anik2000 on 25 Apr 2017, 06:22, edited 1 time in total.
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Re: Jolene entered an 18-month investment contract that  [#permalink]

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New post 25 Apr 2017, 06:21
PareshGmat wrote:
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

after 2nd 6 month why not 10000+10000+200? because we have our intial amount 10000 and the we get 10200. plz explain
Re: Jolene entered an 18-month investment contract that &nbs [#permalink] 25 Apr 2017, 06:21

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