Jolene entered an 18-month investment contract that

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

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Hope it helps.

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.

Great elimination method if I am low on time. Thanks!

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

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.

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).

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

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:

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

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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

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?

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.

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

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

Yup, I think only when the question states per annum is the rate per annum.