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

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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

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;

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?

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

Merging similar topics. Please ask if anything remains unclear.

P.S. PLEASE ALWAYS POST ANSWER CHOICES FOR PS PROBLEMS. _________________

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

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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.
_________________

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.

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!

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

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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

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

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14 Oct 2013, 08:01

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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

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

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.
_________________

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

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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

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

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22 Sep 2014, 22:46

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)

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

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24 Sep 2014, 05:58

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).
_________________

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

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25 Sep 2014, 02:12

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?

gmatclubot

Re: Jolene entered an 18-month investment contract that
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25 Sep 2014, 02:12

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