For some this is the most “interest”ing concept on the Revised GRE (at least for those with a fondness for bad puns). For most, compound vs simple section can be a nuisance. Many think, what is the difference between the two, and/or how did that formula go again?

But remember, this concept involves money, and for many that means its practical (especially if you invest money yourself). But enough rambling…

## Simple Interest

Principal: The Amount of Money initially invested

Interest Rate: The amount return on an investment expressed as a percent of the principal.

Time: The length of time in which a principal is invested

## Sample Problems

1. John invests 100 dollars in account that yields 8% simple interest annually. How much money will John have in his account after one year?

(A) $4

(B) $8

(C) $104

(D) $108

(E) $110

2. Bob invests 100 dollars in a fund that yields 15% simple interest monthly. If Bob invests the principal in the middle of January, which is the first month will he have more than $200 total?

(A) June

(B) July

(C) August

(D) February

(E) March

3. In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210

Answers:

1. D

2. C

3. D

## Compound Interest

Okay, that was the easy part. Now for compound interest. In compound interest things become complicated. We no longer have a nice, clean linear increase. To illustrate:

If Mike invests $100 at 10% simple annual interest, he will have $110. After two years he will have $120. That is his money grows by $10 every year. After 10 years, Mike will have doubled his money.

Now, let’s say Mike’s friend Thomas invests $100 at a 10% rate that is compounded annually. After one year, Thomas will have made the same amount as Mike. But then things start diverging. Remember how Mike always gets 10% of the original 100 (the original 100 is called the principal)? Well, Thomas – because things are getting compounded annually – gets 10% of whatever the value of the account is at the end of the year. Let’s see how this plays out over time.

1^{st} year: 10% of 100 = 110

2^{nd} year: 10% of 110 = 121

3^{rd} year: 10% of 121 = 133.10

4^{th} year: 10% of 133.00 (rounding down) = 146.30…

After 10 years, Thomas will have made $260, which is $60 more than Mike.

Okay, that may all seem like chump change, but the same percent increase applies to numbers with a few more zeroes thrown in. How would $260,000 vs. 160,000 sound?

Of course the point of this lesson is to understand the conceptual difference between the two forms of interest—and not to have you running to the nearest ban, since the numbers above are very generous.

Now for the fun part: Notice how, in the case of Thomas, I seemed to be doing mathematical wizardry. After all, how did I know that 10% compounded annually at 10 years is going to yield 160% of the principal? Well, let’s meet the formula:

V = Total Value

P = Principal

r = annual interest rate

n = number of times per year invested

t = number of years

Pretty unpleasant, no? Well, let’s try to put the formula to the test. And you may want to get your calculators out (this is the Revised GRE after all!)

If $10,000 is invested at 10%, compounded semi-annually, how much will the investment be worth after 18 months?

(A) 11,500

(B) 11,505

(C) 11,576.25

(D) 11,625.30

(E) 12,000.50

Now don’t worry about the semi-annual bit—it just means twice a year. And remember the *n* from the scary little formula above: the number of times per year invested. And that 18 months? That corresponds to t, the number of years, which translates to 1.5.

.

That was easy—once you know where to put everything (and provided you remember the formula)!

How can I do the compounding interest math quickly in GRE? Also, GRE calculator does not support Power function

Hi Fahran,

Most GRE questions on compounding interest are really testing your understanding of the concept of compound interest, not the specific calculation. As long as you understand the concept of compound interest and are familiar with the formula, you should be fine 🙂

What about compound interest calculated annually and withdrawn in 6 months?

Say, P=3500, r=0.04.

Hi Jatin! Do you mean that it’s compounded annually but you take the money out early at 6 months? That would just be V = 3500(1 + (.04/100))^0.5. You set up the regular compound interest equation with .04 annual interest and invested once a year. The only difference is that instead of an exponent of 1 you have an exponent of 0.5. You only did half of the total year. Hope that answers your question!

Hi, thank you for this post.

I have a question about the compounding interest problem at the end of the article. If the question is asking for a 10% increase annually, then why shouldn’t we calculate the square root of 10 to calculate the semi-annual interest rate, instead of dividing it by 2.

In other words, suppose we want to calculate the answer to this question but for a 12 month period. In that case, (1.05)^2=1.1025 , which means 10.25% increase, instead of the 10% requested in the question.

I would appreciate if you could clarify this for me.

Hi Reza,

I’m not sure if I understand your questions, so please bear with me as I try to clarify this a bit! I don’t see where we are dividing by two here–can you be a bit more specific? To be clear, the rate at which interest is compounded does not change over time. In this case, the semi-annual interest rate is 10%–that doesn’t mean that a different amount is charged at the 6 month mark and then at the 12 month mark. What changes is the amount of principle that the interest rate is applied to.

If we were to solve this equation for a 12 month period instead of a 6 months period, we would just need to change one of our variables:

– n still equals 2

-r still equals 10

-P still equals 10,000

– t= 1 (this is the only number that changes)

So, we would have 10,000*1.05^2, which equals 10*000(1.1025). The answer would be 11,025.

If I missed something or misunderstood your question, please let me know!

Hi, thanks a lot for the detailed answer.

Sorry if I didn’t elaborate on my question. By dividing by 2, I was referring to n (number of times per year invested) in the denominator which because the question is asking for compounding semi-annually, as you said, that would mean n = 2.

What I meant by my question is that even in the formula we say r = annual interest rate = 10%, but after calculating the result for a 12 month period, the overall annual interest rate is higher than 10%, and it is, as you calculated, 10.25%. I know that by increasing n (number of times per year invested), this figure (10.25% or true annual interest rate) will even go higher. So what I don’t get is why the question doesn’t simply give us the interest rate for the basic length of time in which the principal is invested, which in this case is 6 month, so that we wouldn’t have two conflicting (I guess!) numbers.

P.S: I made a mistake when I said for reaching a semi-annual interest rate that will result in an annual interest rate of 10%, we should calculate the square root of 10. Instead, I think we should say:

V = P(1 + x/100)^y

V = Total value

P = Principal

x = interest rate for the desired period (in this case, 6 months)

y = number of desired periods (if we want to calculate the result for 12 month period, y = 2)

So if we want to reach a total 10% annual interest rate through compounding semi-annually:

(1 + x/100)^y = 1.1

(1 + x/100)^2 = 1.1

so x = 4.880884817

Thus, I think the question, in the first place(!), should give us this x = 4.880884817 as the interest rate for a 6 month period, instead of giving us a 10% annual interest rate and asking us to consider it for 6-month periods.

Thank you very much for considering my voluble reply.

Hi Reza,

I can answer this follow up question of yours! 🙂 You’re right that if the problem had given you an x value of interest for a single 6 month period to begin with, the figure for 18 months, three 6-month periods, could have been calculated with the same results. So why didn’t the problem in the post do this? The simple answer is that the GRE test itself will not do this– on the GRE compound interest word problems will look at periods in terms of whole years or equal fractions of a year (times per year). Actual lenders and banks will also treat compound interest in this way– interest compounding four times a year at x annual rate, not interest compounding every three months at x interval rate, for example.

In short, the final problem in this post is following the conventions of the GRE, which in turn follows the conventions of the actual finance industry. But you certainly could solve the problem your way, if you first solve for the interest rate of the shorter interval (6 months for compounding semi-annually, 3 months for compounding quarterly, etc.).

Please explain Q#3 of simple interest. I am unable to solve that one.

Simple interest means — you make the same dollar amount in interest every year.

From 2006 to 2008, in two years, John made $20, so that means, he makes $10 every year. Notice that y is a percent, so even though we currently know the dollar amount of simple interest, we don’t know what it is as a percent of the original principal. We can follow back to the starting value.

2008 —-> $270

2007 —-> $260

2006 —-> $250

2005 —-> $240

2004 —-> $230

2003 —-> $220

2002 —-> $210

2001 —-> $200

So, the starting amount in 2001 was $200. Therefore x = 200.

Now, the interest of $10 is what percent of $200? Well, $10 is 5% of $200. So y = 5

x + y = 200 + 5 = 205

Hello guys! where can i find answers?

Hi Reem,

The answers are rather easy to miss, but they came immediately after the questions:

Answers:

1. D

2. C

3. D

50000$ is invested into two portion first one is at 6% simple interest for 3 years and another portion is at 4% compound interest for 2 years and the interest is 4500$. What is the simple principal and initial compound principal? (please someone solve this with verification for me)

Hi Proloy,

Can you please provide me with more information about where you found this question? We are a small team, and we can only provide support for questions that come from Official GRE sources or our own Magoosh material. Perhaps another reader can help you out with this question, but otherwise the formulas provided here should help you to determine the answer 🙂

Hi Chris. I do not understand how the answer is C in the second simple interest question. If the formula for calculating simple interest is I(Interest)= P(Principal) x (R(rate) x T(time), then the answer should be 100*15/100*12 = 180 and so Bob should have more than 200 in the February, which is (D) not August (C). Could you please explain further?

Hi Tiwa,

I think there may have been some confusion about how to apply this formula! You can find the simple interest formula in this blog post:: V=P(1+(rt/100)). For this question, we need to find out how much time passes (t) until the total amount (V) reaches 200. This gives us the following expression which we can simplify:

200=100(1+(15*t)/100)

200=100(1+.15t)

200=100+15t

100=15t

6.66=t

This means that he will have over $200 in the account after 6.66 months have passed–which in this case means 7 months must pass, because the interest is only compounded each month. This is why (C) August is the best answer!

However, there is a much simpler way to solve this question so that you don’t have to do any calculations at all! With simple interest, the same amount is deposited every month because the interest amount is based only on the principle. This means that each month, 15% of the principle ($100) will be added to the account. This is $15 per month. We originally had $100 in the account, we need $100 more to make it to the goal of $200. So, how many deposits of $15 are needed to add $100 into the account? If we divide 100 by 15, we get the same answer of 6.66 which leads us to (C) as well!

I hope this helps to clear up your doubt 🙂

I am confused on this question as the answer suggests 7 months must pass before he has over $200, yet August is the 8th month of the year. Why is the answer not July? (B)

Hi Cameron,

Remember here that in the first month (Jan), he still only has 200 dollars in his account, so it will actually be in the 8th month that he goes over the $200 mark. Here’s the breakdown:

Jan: 200

Feb: 215

Mar: 230

Apr: 245

May: 260

June: 275

July: 290

Aug: 205

So the account doesn’t actually tip over the $200 mark until August!

Hi Chris,

I have a question.

Can you have simple interest calculated semi annually?

I believe so say then principle 100 at 15% annually calculated semi annually then

if no payments made then interest would be 107.50 I believe or would it actually be 115.00?

Then the next six months goes by would the interest then be only calculated on the principle 100?

Thank you

Hi Michael,

Yes, you can calculate simple interest with any time period (1 day, 2 weeks, 1 month, 6 months, 1 year…) as long as you use the formula correctly!

If 15% simple interest on 100 is compounded every 6 months, then after six months the amount would be $115.00. Because it is simple interest, we would just add $15 during each payment period (which is 6 months in this case). That means that after 1 year, you would have $130, and after 18 months, you would have $145, etc.

With simple interest you calculate the amount using only the principle! With compound interest, you would have to calculate the amount based on the principle and any interest already accrued.

can you plug in the numbers and elaborate?

For instance, when i use the formula to get the answer for after a year i get 115 but that should be the answer for after 6 months =/

V = P(1+rt/100)

V = 100 (1+15/100 *1 )

V = 100(1.15)

V = 115

i’m getting confused with the difference between t and n when it comes to simple and compound interest problems

Hi Anna,

The simple interest formula is a bit tricky. In this case, the “t” doesn’t refer to a time measurement like months or years, but rather the number of times that interest has been added to the principal! In this example, the interest is added every six months. After six months have passed, interest will be added the first time, in one year it will be added a second time, in 18 months a third time, etc.

So, we can find the interest after one year using this formula. In this example, t=2 because it’s the second time that interest has been added:

V = P(1+rt/100)

V= 100(1+ (15*2)/100)

V= 100(1+30/100)

V=100(1.3)

V=130

After a year, $130 will be in the bank. The ‘n’ in the compound interest formula, on the other hand, refers to how many times the interest is compounded per year. So if the interest is compounded every 6 months, the n would be 2 in the compound interest formula because the interest is compounded twice a year.

This is an example of a time where conceptual understanding is better than memorizing a formula. As you’ve noticed, the simple interest formula can be confusing or difficult. However, we can just think of simple interest as “simple addition.” After each specific time period, the same amount is added to the bank. The amount is based on the interest and the principal amount. In this case, $15 is added every 6 months. As long as we understand how simple interest works, a formula is unnecessary!

In the last compound interest example problem, if the interest rates get compounded Semi-annually every six months, then why we shouldn’t take (n = 3) instead of (n=2)?

Please clarify…Thanks in advance.

Hi Ahkam,

Good question! n = number of times per year and there is no way for there to be more than 2 6-month periods in a year. We multiply by the 1.5 for our number of years, which brings our exponent to 3, but the value for n still stands. I hope that clarifies! 🙂

Hello,

if n*t = large number

where large number is like 13, 23,32 and multiplier is like 1.05, 1.03, 3.67 then how can i calculate fast using P (1+r/n)n*t

Hi Rumi,

The quick answer is that the GRE will not expect you to do a calculation like that. It is beyond the capability of the calculator and reasonable mental math skills. If you do end up with a calculation like this, there are two possibilities. One is that you have made a mistake and the question is looking for a more simple or ‘elegant’ solution. The second is that you should estimate the answer by rounding the exponent to the nearest whole number. If you are supposed to estimate, then the answer choices would likely be far enough apart that you could distinguish the correct answer after estimating. However, it is extremely unlikely that you would be given a question that requires you to complete a calculation like this!

Sorry, I’m having trouble with the last compound interest question. When I solve V = 10,000(1+ 10/200)^(1.5)(2) I get 12,155.0625. Am I doing some order of operations wrong?

Thanks for your help!

Hi Liz,

This may be the problem, so let me try to walk through the calculation and maybe you can see where you went wrong!

=10,000 * (1 + 10/200)^(1.5)(2) [Calculate “10/200”]

=10,000 * (1 + 0.05)^(1.5)(2) [Add “1” and “0.05”]

=10,000 * (1.05)^(1.5)(2) [Calculate “1.5 * 2”]

=10,000 * (1.05)^3 [Calculate “(1.05)^3”]

=10,000 * 1.157625 [Calculate terms]

=11,576.25

Hi there, I was wondering why you did 10 instead of .10 because it did state in the sentence that it was invested at 10%

That’s a great question, Michael. 🙂 The reason we plug 10 in for the value of

r, rather than .10 is simple– we are plugging in the interest rate, which is expressed as a percentage, andnotas a decimal that corresponds to a percentage. So the number for the interest rate will always be more than one, unless the percentage itself is less than one percent.Does this make sense? If you still have any doubts, just let me know. 🙂

Hi Chris, I am not so clear why r should be divided by 100. I mean, r is already the annual interest rate like 5%. Or does it alternatively mean in GRE test that annual interest rate merely stand for the number of a percent (like the 5 of 5%)?

Thanks a lot for helping me with this! 🙂

Hi Susan 🙂

In the equation on this post, r refers to annual interest rate expressed as a percent. For example, if the question said that the annual interest rate were 5%, then r = 5. So, in the equation, we need to divide by 100 in order to rewrite the interest rate as a decimal:

interest rate = 5%

r = 5

r/100 = 0.05

That said, since the GRE doesn’t test the equation directly, if you wanted, you could define r as the interest rate as a decimal. In that case, you would not divide by 100 in the equation:

V = P(1+r/n)^(nt)

r = annual interest rate expressed as a decimal

So, if the annual interest rate were 5%, r = 0.05.

Either way works when using this equation. You just have to make sure that in the end, you are adding the interest rate expressed as a decimal to 1 in the parenthesis!

Hope this clears up your doubts 🙂

It is the number which divided by 100 not really. Because the meaning of word percent is per or one of cent or hundred. So if you want to find 8 percent of 200 than

Think that there are 200 apples which should be distributed between 100 persons. Than 8 persons will get how much apples?

One person out of hundred get 200/100

Than 8 persons out of hundred get (200/100)*8

Can you please provide the solution to this problem.

In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210

thanks..:)

Hi Akash,

I’ll just quote Chris from another comment here in the thread: “Sure, I saw that the difference between ’06 and ’08 was $20. Thus each year is a $10 increase since are dealing with simple interest. If the accounted started in 01′ that means in 5 years (from ’01 to ’06), the account went up $50 (ten each year). So in 2001 account was $200 = x. If account increases $10 that is 5% of 200. So y =5. And x + y = 205.” I hope that helps. 🙂

thanks for the quick reply. 🙂

You’re very welcome! Happy studying 😀

I understand the logic behind that solution, but can the simple interest formula be used to solve it?

I tried it and got 4 for Y and 208.xxx for X.

Hi Brian,

So, this will be a longer approach for this problem, but it’s possible. The key will be to remember that the principal can only be “x”. You can create two equation given that you have two variables (x and y) to solve.

The first equation is based on years 2001 to 2006:

I = P * r * t

I = x * (y/100) * 5 [Principal is “x”; Rate is y%; Year is 5]

(250 – x) = x * (y/100) * 5 [Interest is difference from end amount and original amount]

The second equation is based on years 2001 to 2008:

I = P * r * t

I = x * (y/100) * 7 [Principal is “x”; Rate is y%; Year is 7]

(270 – x) = x * (y/100) * 7 [Interest is difference from end amount and original amount]

Finally, you use both equations and solve for one of the variables. Give it a try! Good luck! 😀

I’m still unclear on how to solve this problem I got y=4 and x=208.333. This was based on my using the SI formula twice. Once for a 2-year period and the second time for a 5-year period. Can u please explain?!?

I am having the same issue!

Hi Brian,

The problem that you may be encountering is that you are using “250” as the principal in your equation. However, this CANNOT be. The “250” includes the original principal (“x”) and interest over 5 years (2001 to 2006). For simple interest, the interest in calculated ONLY on the original principal amount (“x”). Whether the end period is 2006 with $250 or 2008 with $270, these are both calculated based on the original principal of “x”. Using anything else as the principal will result in the wrong answer as it includes interest accrued.

Hi,

Will the GRE calculator enable us to perform the last equation (comp. interest). I’m not sure how I will compute ^3….

thanks,

Hi Yasmine,

The GRE calculator is very limited, and if you want to calculate powers, you have to type it manually. So 4^3 would be 4*4*4= rather than a calculation of ^3 directly. This can get very messy with powers that are larger. Because of this challenge, we like to emphasize estimation skills and mathematical pattern thinking!

I hope that helps. 🙂

Hey! Can any body prove why less compounding period results in more interest?

Hi Tian Tuo,

Good question! 🙂

The interest earned

per periodis greater with fewer compounding periods, but the final value of the interest earned is greater with more compounding periods. I hope that clarifies! 🙂Hi there, thanks for all the information first of all.

I have a question about the last example. I tried to solve it without the formula simply multiplying by 1.1 each time so 10,000 x 1.1 = 1,100 , and then 1,100 x 1.1 = 12,100, and then 12,100 x 1.1 = 12,310… which is incorrect but I don’t understand why… Am i not simply compounding the interest each time? 18 months / 6 months = 3 so three compound interests should equal the correct answer?

Any help would be appreciated!

Hi Holger,

You have almost got it! 🙂

You have to divide the interest (10%) by the number of compounding periods per year. Notice how we have a 200 on the bottom of the fraction? (10/200 inside the parentheses.) This is because we are doing two things at once–dividing 10/100 to get the decimal version of 10% and also dividing that by 2 because there are 2 semi annual periods in the year.

The way you are doing the math means that the investment is actually earning 20% interest! (Which would be awesome. :)) I hope that helps.

Thank you thank you thank you! I love it when somebody has already asked my question.

THANK YOU. I was having trouble understanding the video lesson.

Hi Chris,

For Question 3, Though i got 205 as my final answer but with another approach i was trying to calculate y (rate of interest) considering P= $250, R= y% , T= 2 years

So, S.I = (P*R*T)/100

S.I = (250*y*2)/100

S.I = 5y

We got $270 after 2 years

So, Amount = P + S.I

270= 250 + 5y

Therefore, y = 4

However, the correct value for y is 5% but with this approach i got 4%. Please let me know where i am wrong.

Simple Interest is always calculated on the original Principal (‘x’ in this case). But u mistook it for 250/- (which is actually, P + S.I after 5 years).

By your approach,

270 = 250 + (S.I for 2 years)

where, S.I for 2 years = P.T.R/100 = x*y*2/100.

=> 270 = 250 + x*y*2/100

=> x*y = 1000.

As we know John is having $250 after 5 years,

P + S.I for 5 years = $250

=> x + (x*y*5/100) = 250

=> x = 250 – (x*y/20)

(substituting x*y with 1000 from earlier equation)

we get, x = 250 – (1000/20) = 250 – 50 = $200

(substituting x with 200 in x*y = 1000)

we get, y = 5%.

Therefore, x + y = 200 + 5 = 205 which is (D)

I set it up like this:

At some year T, the total balance will be P + PRT.

So for 2006, (@ T = 5), x + x*(y/100)*5 = 250, where y/100 = R.

For 2008, x + x (y/100)*7 = 270. {P + PRT = balance at time T = 7}

After subtracting the two equations, I get x*(y/100) = 10. So principal times rate for one year is $10. I originally started down your path, and ended up with a principal of 208.33, but with 4% interest, you will not get $270 at year 7.

I think the big takeaway is P + PRT = balance at some later time T.

This is a good , subtle problem. Hope this helps – John.

Hi,

Could you explain how you solved the problem you setup above?

Thanks,

Jess

Hi,

I am confused about how to calculate such large exponents while calculating compound interest quickly, as gre calculator doesnot allow such calculations.

But remember, this concept involves money, and for many that means ***it’s*** practical (especially if you invest money yourself). But enough rambling…

Don’t persecute me : ) I know grammar, but I don’t know math!

🙂

how many compound interest and simple interest problems on gre?

You might get one. But that’s probably about it.

Hope that helps!

100* (1+ 15/100 * X) = 200

100 + 15X = 200 => X= 6.6 ( it means after July)

my way is a bit complicated!

do you know another way to solve Q2?

Thanks,

R

Hi Ram,

You def. got it! But a more straightforward/intuitive way is the following: each month $15 is added. 7 x 15 = 105, so he will have to wait 7 months after Jan., which is August.

Hope that helps!

How many of these type of questions are actually on the GRE? I am using the Official Guide to study, and there are some scary looking sample problems regarding compound interest and such. I am nervous because I only learned this stuff in high school using calculator programs!

It does look pretty scary. These question types aren’t that common. My rough estimate is 40% of the tests will have such a question. And typically these questions aren’t as scary looking as some they have in the Official Guide.

Hope that helps 🙂

How do I solve for the exponents without taking the log (in the second simple interest problem for example)? I noticed that the GRE calculator does not have a log button?

Hi Jill,

For the second problem you don’t have to use logs at all, since it is dealing with simple, not compound, interest. Does that help?

the formula is not the same in the video clip

Final = P (1+ r/c)nc

which one should stick to it

Rakan,

Just make sure that the “nc” is in exponent form:

P(1 + r/c)^nc

That should do the trick!

Hi, I am completely aware of the difference between simple and compounded interest. However, will the type of interest be explicit on the test? I took a practice version which did not specify, and there was no way to tell which method was desired.

Hmm…that’s a good question. It typically won’t be explicit but will give you an indication via the question. There shouldn’t be any ambiguities in the problem, though it may seem initially tough to figure out which method is required. Remember to determine whether the sum paid out per month/week/year is the same or if that sum is increasing.

Hope that helps!

Hi Chris,

concerning the first sample problem the answer should be 100$ as the interest is collected annually, i.e. the interest is only added to the whole year and not fractions of it by definition of simple interest, otherwise you will need to define the compounding rate.

thank you.

Oh yes, that’s right! Thanks for catching that :). I’ll make the necessary changes.

Chris you are going to kill me 🙂

what I said was wrong to some extend, I confused the mathematical definition of the word simple interest and compound interest and the collecting rate , i.e it’s ok to collect the simple interest per any period of time (a year or a fraction) as long as he didn’t mention in the question a certain collecting rate ( a constrain that a bank can add or something) I’ll use your example to explain my point

e.g. John invests 100 dollars in account that yields 8% simple interest annually, collected annually, How much money will John have in his account after 26 month?

the answer is 16$

on the other hand if it was 8% compound interest, with a monthly compounding rate, with an annual collecting rate then the answer is

100 x ((1+(0.08/12))^(12 x 2) = 117.288$

I’m sorry for that slip, I wasn’t accurate at all in what I wrote the first time, and I assumed that the interest is collected annually out of the blues I guess 🙂

Hi Amr,

Not a problem. Now I understand what you mean :). Sure, you can have all sorts of different non-yearly intervals with simple interest. It shouldn’t affect anything – the way it does with compound interest.

For the first compound interest problem, is there a faster way to calculate the exponent rather than multiplying it by itself multiple times? It seems rather time consuming

Hi Ben,

Actually, there is not a way that I know of. The good news is that with the calculator it is not that time-consuming. Anyhow, explanations of a concept can often time make the actual solution seem longer than it really is when you are simply punching the numbers into the calculator. One alternative though, if you don’t use a calculator, is to look at the answer choices. Usually two are three of them will not match with the numbers given in the question (e.g., round numbers when the answer clearly calls for a decimal).

Hope that helps :).

Thanq very much chris giving good stuff and i suggest u to give more questions like this…

Shiva,

Thanks for the kudos :). An advanced interest post is definitely called for in the not too distant future.

Chris,

Can you explain the solution of Q2.

The question is basically saying that John earns $15 per month (on top of his 100). Thus it will take him 6.67 months to earn 100. Since he start investing at the beginning of January, he will earn 100 by the end of July.

Hope that helps 🙂

Wait, are you saying that when it says “monthly,” we still assume his account balance increases daily/hourly/etc? I understand that it’s 6.67 months, so technically it’s the end of July. But isn’t that assuming that the bank deposits his interest earnings every day or every hour, as opposed to the beginning of each month?

Thanks.

I had the same doubt.

As the account yields 15% interest monthly, shouldn’t the interest be reflected when a new month starts?

Hi Manan,

I responded to Zuhaib’s comment. Again, sorry for any confusion :).

Hmm, that is a good point. I was assuming that it increases every minute, but technically ‘monthly’ would mean only at the beginning of each month. So not the best question – my assumption would be far more valid if the question dealt with a constant growth rate, such as a population of bacteria.

Sorry for any confusion :).

Hi Chris,

So if we say that interest is added at the beginning of the month then the answer would be August, right? As he still has $190 at the beginning of July.

Also, this blog seems to have a few typos.

1. Q2 first it’s John then you say Mike!

Intro to compound interest: you state, after 10 yrs, mike will have 260, which is 60 more than mike

Wouldn’t that be bob has 260, which is 60 more than mike.

Thanks.

Btw, thanks for these blogs and comments. they’re very helpful!

Oh wow, you’re right! That is very confusing :(. Note to self: do not use really generic names :).

Thanks for catching that Shamila!

Dear Chris,

Thanks for the discussion however, I am confused with your response regarding question# 2. According to the question, the investment took place in mid-January, NOT beginning of January, therefore the first $15 supposed to be earned by mid-February…am I right? While it takes 6.67 months to earn $100 with the given simple interest rate therefore the value $200 never be reached until late first week of August.

Hi Milon,

Sorry for the confusion — I changed the wording from beginning of Jan to mid-Jan. last time I edited the post. Therefore, it kind of invalidates much of what I (and the other users) said in the comment post.

Yes, you are right. The first amount will be earned in mid-Feb. and the 200 won’t be reached till the first week of Aug. There is also some ambiguity about whether the simple interest is paid only at the beginning (or now that I’ve changed the question) the middle of the month. In the latter case, the answer will still be Aug. That’s why I changed the verbiage.

Again, sorry for any confusion :).

Hi Chris!

I’m confused with the second question still!!! Is the growth rate constant? As in..15% on 100 is 115 during feb mid! So the next will be calculated as 15% on 115 right? Or it is constantly increasing? moreover, how can the answer be Aug? Because 200 would be collected by mid of July! I’m seriously confused!! 🙁

Sorry for any confusion :).

The amount is invested at simple interest, meaning that $15 dollars will be added to the account at the middle of each month. So it will take 7 months (7×15). Therefore, seven months after the middle of January is the middle of Aug.

Hope that helps!

Hey Chris..I got that part..but what about the growth rate? Is it constant? As in..15% on 100 is 115 during feb mid! So the next will be calculated as 15% on 115 right? Or it is constantly increasing?

Also, in such type of questions, will they specifically mention if the rate is constant?

Ankita,

Sorry that was confusing :). No, the growth rate is not constant but is only calculated on the 15th.

Hope that helps!

Chris:

Do you mind showing the steps you used to solve it? Thanks

Sure, I saw that the difference between ’06 and ’08 was $20. Thus each year is a $10 increase since are dealing with simple interest. If the accounted started in 01′ that means in 5 years (from ’01 to ’06), the account went up $50 (ten each year). So in 2001 account was $200 = x. If account increases $10 that is 5% of 200. So y =5. And x + y = 205.

Hi Chris,

Thank you for the explanation. How come y isn’t equal to 0.05? I thought the 5% would have to be added in decimal form, with x + y equaling 200.05.

Thanks!

Hi Helena,

That’s a tricky one! See the variable is presented as “x percent”. In this case, the number for x is simply 5, as in 5 percent. As an actual number, 5% is represented as .05, but if ‘x’ were to equal .05, we would have .05 percent, which is .0005.

Hope that clears things up :)!

Hi Chris:

How did you come out with option E (210) on question 3?

Oops, that should be (D) 205

x = 200 and y = 5

Thanks for noticing that :).

Hi Chris, this is again regarding Q3.

Please clarify how did you calculate y=5. kindly let me know how you feel about the solution below. I feel the answer should be “E”

The balance in the account in 2006 is $250 which increases to $270 in 2008. Since this questions deals with Annual Simple Interest, we can calculate that interest earned per year is $10.

Thus in 2005 a/c balance = $250 – $10 = $240 ….

So in 2001 a/c balance should be $200.

So x+y should fetch 200+10 = $210.

Hi Abhijeet,

Notice the questions says ‘y’ percent. If ‘y’ were 10, then 10% of 200 is 20, which would lead to an increase of $20 per year, not $10 (or 5%), as the question states. Therefore, y must equal 5.

Hope that helps :)!

Hi Chris,

Sorry, my mistake !!

I mistook ‘y’ to be the annual interest that accrues every year on the principal of $200. $10 is definitely is 5% of $200.

Thanks,

Abhijeet

No problem :)!

Hi Chris,

I still feel the answer should be $210(200+10) or the question needs to be rephrased to “y % simple interest annually”. If we are saying “y simple interest annually”, one expects to calculate the interest rather than the rate. Correct me if I am wrong.

Thanks,

Aditya

Yes, that should be y%. Now I see why this one confusing so many people.

Thanks for point that out :)!

hello

I am very confused about the sample question 3. I find it very hard. Can you please explain me.

I am very weak in math. would appreciate your help.

Hi Sukaina,

Just a note that I’ve sent your question to our remote tutors, who will respond to you via email! As a Magoosh premium subscriber, you can click on the ‘Help’ tab on the left side of your screen or email help@magoosh.com for these types of questions in the future!

Thanks!

Jessica

Oops, that’s a typo. I’ll take care of it. Thanks for pointing that out :).

Hi Amy :).

Yes, that’s definitely a series of typos. Thanks for catching that!

As for r, it can stand for ‘compounded annually’ as long as there is the n (number of times compounded annually). Therefore 10% compounded semi-annually works out to 5%: (10/100(2)) = 1/20. So either way works.

Hey Chris,

Is it the word ‘ compounded ‘ that decides.the fate of the question or some other words are also included in the.pool..?

For compounded interest questions, ‘compounded’ determines the fate of the question.