BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Interest and principle

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Fri Mar 05, 2010 9:50 pm
Thanked: 1 times

Interest and principle

by muralithe1 » Sun Jul 04, 2010 10:01 am
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
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Sun Jul 04, 2010 10:11 am
Let the initial amount be 100
interest are paid in th eorder - 2,3,4

after 2 - 100 + 2 = 102
after 3 - 102 + 3.06 = 105.06
after 4 - 105.06 + 4.2024 = 109.2624

so for 100 he got 9.2624 interest.

For 10000 he will get, 926.24

Pick E
Top
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Fri Mar 05, 2010 9:50 pm
Thanked: 1 times

by muralithe1 » Sun Jul 04, 2010 10:16 am
Thanks kvcpk.
You are correct according to the official answer. But my doubt here is in the simple interest formulae of PTR/100...What u have put for 'T'???
Top
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Sun Jul 04, 2010 10:20 am
The percentage calculations I made are all made orally.. You do not really need a Pen/calculator everytime you need to do a percentage calculation.

suppose you want to know what is 60% of 30..
Do not do like this:
60*30/100 = 1800/100 = 18

You just need to multiply the two numbers immediately..
what is 60*30 = 1800

You will roughly know that it willnot be 1.8 or 180.. so it is 18.

This example might look silly because the numbers are too easy..

Lets see a bit complex one..

what is what is 20% of 342?
before you make a calculation.. just multiple 2 with 342 = 684.. so it wil be 68.4

what is 24% of 500? just do 24*5 = 120.. done

One more suggestion I give you is that when ever there are percentage problems.. first see if it is possible to take the complete unit as 100. Then calculations look easy.. just as in the above problem..

Hope this helps!!
Top
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Sun Jul 04, 2010 10:31 am
muralithe1 wrote:Thanks kvcpk.
You are correct according to the official answer. But my doubt here is in the simple interest formulae of PTR/100...What u have put for 'T'???
Here we do not need a formula.. it is more of logic..
Problem clearly says, 2% interest at the end of 6months
So on the amount that is present, you will get 6% at the end of 6 months

Simple interest is a case where in there is interest credited over a period of time.. not at the end of the period.
So this case is not the same as simple interest case.
[Experts - Correct me if I am wrong]

Even in the case you want to use the formula, T in all these cases will be 1 for the above reason.

so in PTR/100, p=10000, T=1, R = 2
PTR/100 = 200
This is the interest that will be paid for the first time.

Similar case for the others too..

Hope this helps!!
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Sun Jun 06, 2010 7:21 pm

by bikash123 » Sun Jul 04, 2010 3:46 pm
This question created a confusion in my mind. Since the time period is six months for the interest payment, we need to calculate interest for six months rather than simply multiplying the principal amount with the givn interest rate.

Could you please let u know about the source of this question. If we take the time period of six months to calculate the interest, we get the interest amount of 456.53
Top
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Fri Mar 05, 2010 9:50 pm
Thanked: 1 times

by muralithe1 » Sun Jul 04, 2010 8:43 pm
Well this is from MGMAT cat4.. too was in doubt jus tlike you about he calculation..Usually interetst will be stated per annum..So for 6 months..t=6/12 = 1/2...

Not quite sure..Please some body clarify
Top
Master | Next Rank: 500 Posts
Posts: 265
Joined: Mon Dec 28, 2009 9:45 pm
Thanked: 26 times
Followed by:2 members
GMAT Score:760

by mj78ind » Sun Jul 04, 2010 10:34 pm
bikash123 wrote:This question created a confusion in my mind. Since the time period is six months for the interest payment, we need to calculate interest for six months rather than simply multiplying the principal amount with the givn interest rate.

Could you please let u know about the source of this question. If we take the time period of six months to calculate the interest, we get the interest amount of 456.53
I agree, it should be 456.53. The first six months interest is 2%, then next 6 months int on principal and int of 1st 6 months is 3% etc.
Top
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Sun Jan 24, 2010 2:29 pm
Thanked: 3 times

by jeremy8 » Mon Jul 05, 2010 2:09 am
The way I see it, the 6 months timeline doesn't matter. It could be at the end of the week, for all we care.
What it means is that the investment plan is offering her 2% interest on her capital 6 months after she enters the plan.

So after the first sixth months, she makes 200$ on her 10k. She reinvests 10,200$ (initial capital + interest, which is what they mean by "each interest payment is reinvested in the contract") over the next 6 months and gets 3% on that, or 306$ for a total of 10,506$.
Finally she reinvests her 10,506$ for the last 6 months, getting 4% interest, or 430.24$, bringing her total to 10,926.24$

You can change the 6 months timelines to 6 years, 6 days, 6 minutes, it doesn't matter. The timeline is completely arbitrary and irrelevent. What matters is just the chronological order in which the different interest rates affect the capital invested.
Top
Master | Next Rank: 500 Posts
Posts: 265
Joined: Mon Dec 28, 2009 9:45 pm
Thanked: 26 times
Followed by:2 members
GMAT Score:760

by mj78ind » Mon Jul 05, 2010 2:29 am
jeremy8 wrote:The way I see it, the 6 months timeline doesn't matter. It could be at the end of the week, for all we care.
What it means is that the investment plan is offering her 2% interest on her capital 6 months after she enters the plan.

So after the first sixth months, she makes 200$ on her 10k. She reinvests 10,200$ (initial capital + interest, which is what they mean by "each interest payment is reinvested in the contract") over the next 6 months and gets 3% on that, or 306$ for a total of 10,506$.
Finally she reinvests her 10,506$ for the last 6 months, getting 4% interest, or 430.24$, bringing her total to 10,926.24$

You can change the 6 months timelines to 6 years, 6 days, 6 minutes, it doesn't matter. The timeline is completely arbitrary and irrelevent. What matters is just the chronological order in which the different interest rates affect the capital invested.
,

Ok another doubt 2% on 10k for 6 months will give 100 as interest, similarly 3% on ~10.1 K will give 150 in 6 months etc.
hence the answer should be around ~450 ...
Top
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Sun Jan 24, 2010 2:29 pm
Thanked: 3 times

by jeremy8 » Mon Jul 05, 2010 2:54 am
mj78ind wrote:
Ok another doubt 2% on 10k for 6 months will give 100 as interest, similarly 3% on ~10.1 K will give 150 in 6 months etc.
hence the answer should be around ~450 ...
How do you come up with 2% of 10k = 100$?

2% of 10k is 200$, 3% of 10,200$ is 306$, etc...

2% of 10,000 is the same as saying 2*10,000/100, or simply 2*100.

I don't really know how to say this. I'm not trying to put you down or anything, maybe you're just really tired.
I make crazy mistakes when I'm really tired too, but I would suggest really studying your arythmetic fundamentals if you think 2% of 10k is 100$ and if it's not obvious you made a mistake.
Everything is based on your foundations. If your foundations are weak in one way or another, anything you build on them will be weak as well, since it'll directly depend on the strenght of your foundations.
Everything you do in math and on the GMAT is directly affected by your ability to deal with numbers as comfortably as possible, and arythmetic is really the base of that.
You only have so much brainpower to allocate to whatever problem you're working on, and if you have to use some of that brainpower to check that you're not making mistakes on easy calculations, that's seriously going to affect your problem-solving abilities negatively, especially in a time-constrained context.
It would not be wise to try to deal with more advanced concepts if you are still struggling with certain basic relationships between numbers.

I would suggest going to Khanacademy.org

It's an amazing website. The owner is an incredibly intelligent guy who designed more than 1000 tutoring videos by himself and has 3 Masters degress, two from MIT and an MBA from Harvard...
The videos are extremely well explained, and based on the idea of truly understanding the underlying logic behind every concept.
He also has a section where he goes through every quant problem in the OG, and that's really helpful as well.
You can rewind the videos at will and go over certain sectoins as many times as you want, etc....
This really helped me when I started learning math again and I'm sure it'll help you as well.
Top
Master | Next Rank: 500 Posts
Posts: 265
Joined: Mon Dec 28, 2009 9:45 pm
Thanked: 26 times
Followed by:2 members
GMAT Score:760

by mj78ind » Mon Jul 05, 2010 3:02 am
jeremy8 wrote:
mj78ind wrote:
Ok another doubt 2% on 10k for 6 months will give 100 as interest, similarly 3% on ~10.1 K will give 150 in 6 months etc.
hence the answer should be around ~450 ...
How do you come up with 2% of 10k = 100$?

2% of 10k is 200$, 3% of 10,200$ is 306$, etc...

2% of 10,000 is the same as saying 2*10,000/100, or simply 2*100.

I don't really know how to say this. I'm not trying to put you down or anything, maybe you're just really tired.
I make crazy mistakes when I'm really tired too, but I would suggest really studying your arythmetic fundamentals if you think 2% of 10k is 100$ and if it's not obvious you made a mistake.
Everything is based on your foundations. If your foundations are weak in one way or another, anything you build on them will be weak as well, since it'll directly depend on the strenght of your foundations.
Everything you do in math and on the GMAT is directly affected by your ability to deal with numbers as comfortably as possible, and arythmetic is really the base of that.
You only have so much brainpower to allocate to whatever problem you're working on, and if you have to use some of that brainpower to check that you're not making mistakes on easy calculations, that's seriously going to hamper your problem-solving abilities.
It would not be wise to try to deal with more advanced concepts if you are still struggling with certain basic relationships between numbers.

I would suggest going to Khanacademy.org

It's an amazing website. The owner is an incredibly intelligent guy who designed more than 1000 tutoring videos by himself and has 3 Masters degress, two from MIT and an MBA from Harvard...
The videos are extremely well explained, and based on the idea of truly understanding the underlying logic behind every concept.
He also has a section where he goes through every quant problem in the OG, and that's really helpful as well.
Jeremy my man, my man! I know am not a smart mortal, let's look at it once more:

Simple Interest formula = P*R*T/100 where P = principal, R = Rate as a %, T = time in years.

Now, P = 10,000 R = 2% T = 1/2 years

So input in the formula = 10,000*2*1/(2*100) = kinda looks like 100 to me ....... do not know if the maths fundamentals have changed but the last time i checked the above equation would have given me a 100....... and so for the rest. Confidence is good but misplaced confidence can lead to a low score when expectations are high and man that kills!
Top
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Sun Jan 24, 2010 2:29 pm
Thanked: 3 times

by jeremy8 » Mon Jul 05, 2010 3:23 am
mj78ind wrote: Jeremy my man, my man! I know am not a smart mortal, let's look at it once more:

Simple Interest formula = P*R*T/100 where P = principal, R = Rate as a %, T = time in years.

Now, P = 10,000 R = 2% T = 1/2 years

So input in the formula = 10,000*2*1/(2*100) = kinda looks like 100 to me ....... do not know if the maths fundamentals have changed but the last time i checked the above equation would have given me a 100....... and so for the rest. Confidence is good but misplaced confidence can lead to a low score when expectations are high and man that kills!
Ok, I understand what you're saying. I'm sorry if my post came out wrong, I was really just trying to help you because trust me, I can very easily relate to not being comfortable with math...
Fwiw, this website is still more than worth checking out for all the reasons I mentioned, most importantly the underlying logic part.

I think your mistake comes from the fact that you assume that they're giving you a yearly rate that you have to divide by 2 using that formula.
If they said she was getting 2 percent a year and then asked you how much she got after 6 months, it would be different.
But there's not mention of a yearly rate. The rate is 2% after 6 months, period, so there's no need to use that formula.
Think about this: If I say "give me 10$ to invest and in 7 days, I'll give you 2% interest on these 10$".
Are you going to assume that this is a yearly rate and plug it into the forumla as 2/52 weeks?
You're just going to calculate that after 7 days, you have made 20 cents of interest on your 10$.
It is the same here.
You're confused by the 6 months timeline, because it's much closer to one year than 7 days is, and that's exactly why the GMAT is using it to confuse people. Be careful with formulas. Always make sure you really understand what they mean and what you're plugging into them.
Top
Master | Next Rank: 500 Posts
Posts: 265
Joined: Mon Dec 28, 2009 9:45 pm
Thanked: 26 times
Followed by:2 members
GMAT Score:760

by mj78ind » Mon Jul 05, 2010 3:39 am
jeremy8 wrote:
mj78ind wrote: Jeremy my man, my man! I know am not a smart mortal, let's look at it once more:

Simple Interest formula = P*R*T/100 where P = principal, R = Rate as a %, T = time in years.

Now, P = 10,000 R = 2% T = 1/2 years

So input in the formula = 10,000*2*1/(2*100) = kinda looks like 100 to me ....... do not know if the maths fundamentals have changed but the last time i checked the above equation would have given me a 100....... and so for the rest. Confidence is good but misplaced confidence can lead to a low score when expectations are high and man that kills!
Ok, I understand what you're saying. I'm sorry if my post came out wrong, I was really just trying to help you because trust me, I can very easily relate to not being comfortable with math...
Fwiw, this website is still more than worth checking out for all the reasons I mentioned, most importantly the underlying logic part.

I think your mistake comes from the fact that you assume that they're giving you a yearly rate that you have to divide by 2 using that formula.
If they said she was getting 2 percent a year and then asked you how much she got after 6 months, it would be different.
But there's not mention of a yearly rate. The rate is 2% after 6 months, period, so there's no need to use that formula.
Think about this: If I say "give me 10$ to invest and in 7 days, I'll give you 2% interest on these 10$".
Are you going to assume that this is a yearly rate and plug it into the forumla as 2/52 weeks?
You're just going to calculate that after 7 days, you have made 20 cents of interest on your 10$.
It is the same here.
You're confused by the 6 months timeline, because it's much closer to one year than 7 days is, and that's exactly why the GMAT is using it to confuse people. Be careful with formulas. Always make sure you really understand what they mean and what you're plugging into them.
Ok my bad! I get it the language is the difference...... Anyways I will check that website.

Cheers
Top
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Sun Jan 24, 2010 2:29 pm
Thanked: 3 times

by jeremy8 » Mon Jul 05, 2010 3:46 am
mj78ind wrote: Ok my bad! I get it the language is the difference...... Anyways I will check that website.

Cheers
You really should; This guy is amazing, I guarantee you'll love his videos.

Good luck with everything
Top
Post new topic Post Reply