Lesson: Simple Interest and Compound Interest

Comment on Simple Interest and Compound Interest

hi brent..
actually u said the principal interest formula was S.I = (principal*rate*time)
but u only explained that in the beatthegmat prblm S.I = principal*(1+rt).

which formula was correct??
gmat-admin's picture

Sorry, can you please indicate which Beat The GMAT question you're referring to. I checked the links above, and I can't tell which one you mean.

sorry .. i misunderstood someone explained with different formula for simple interest i.e A=P(1+rt) which means
t= time
p = principal
r= rate
gmat-admin's picture

The formula A=P(1+rt) computes the TOTAL VALUE of your investment after time t.

The formula S.I = principal*(1+rt) computes the TOTAL INTEREST time t, which you must add to the initial investment (P) to get the TOTAL VALUE.

hi brent... for finding compound interest
C.I= P(1+r)^t. is that correct??
gmat-admin's picture

That formula is for a specific case where r = the annual interest rate and t = the number of years.

The formula shown in the video accounts for all possible compound interests (compounded monthly, biannually, etc).

Hi Brent, do you think it is absolutely necessary to learn the formula for compound interest or is it okay to perform the calculations each time instead? Is it common to see questions with a larger no. of compoundings? I find the latter method to be much simpler.
gmat-admin's picture

The latter method is much easier, but there have been (on rare occasions) official GMAT questions that test your knowledge of the compound interest formula.

Here's one example: https://gmatclub.com/forum/if-1-were-invested-at-8-percent-interest-comp...

Hi Brent!

I've been going through the questions and I am really stuck on questions like this one: "If $1 were invested at 8 percent interest compounded annually, the total value of investment, in dollars at the end of 6 years would be"

In this question, I put the number of compoundings as 6 in the formula, which obviously was wrong. I made the same error in two other questions as well. How do I identify number of compoundings? I consistently get confused between years and number of compoundings.
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-1-were-invested-at-8-percent-interest-comp...

There WILL be 6 compoundings in total.
There is 1 compounding per year, and there are 6 years, for a total of 6 compoundings.

In the formula featured in the above video,
c = the number of times the interest is compounded each year
n = the number of years the investment collects interest

So, for that question, c = 1 and n = 6

Does that help?

BTW, here's my full solution: https://gmatclub.com/forum/if-1-were-invested-at-8-percent-interest-comp...


Hi Brent,
My question is certainly stupid, but I can't see where the flaw is my reasoning.

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

Here is what I did:
1. 270-250=$20
2. $20=250*(y/100)*2(2 years)<=> 1=25*(y/100)<=> y=100/25=4
So y=4%
3. And from here, I=200*0,04*5 <=> I=40

I understand your answer perfectly, but I can't see where I am wrong.
gmat-admin's picture

The key concept here is that, with simple interest, one's annual interest is based on the value of the INITIAL investment.

Example: In 1980, Joe invested $100 at simple interest rate of 10%. So, every year, Joe receives $10 interest (which is added to his initial investment).
40 years later (in 2020), Joe's balance is $500, HOWEVER he still receives only $10 interest each year.

The question tells us that the initial investment occurred in 2001.
In your solution, you're treating the 2006 balance of $250 as the initial investment.

had to say that I was extremely lost in this question


My direction was like switching a lot and get nothing done at the end...
gmat-admin's picture

Question link: https://gmatclub.com/forum/a-photography-dealer-ordered-60-model-x-camer...
This is one of the highest ranked questions (difficulty wise). So, you're certainly not alone.

Were you able to follow the solution(s) provided by experts in the thread?

Yes, it's calculation sensitive I'd say. Don't understand weighted average one, but could follow the formula, which is his profit divided by what he originally paid.
gmat-admin's picture

Good stuff!

Even after going through the comments on GMATClub and referring to various other blogs, my mind is just not able to grasp the concept of when to do what in semi-annual, quarterly, and monthly compound interest... Please help with this question...

gmat-admin's picture

Thank you, Brent :)
It helps. Still, I hope not to see hard compound interest questions in the exam :(

Hi Brent, to clarify in compounding formula..
t > calculate in year : 1,2,3....but if it's 2 months: 2/12
c > calculate in months. Compound monthly mean 12, quarterly mean 4, 2 months mean 2. My silly question is can c go over 12 like compound 24 monthly?

Thanks Brent
gmat-admin's picture

I haven't seen the GMAT test-makers go over 12 compoundings per year, but it's conceivable.
In fact, we could have daily compoundings (for a total of 365 compoundings per year).

Thanks Brent. Good point you mentioned compounding daily, if that is the case, will we write C as 365/12 ?
gmat-admin's picture

c = the number of times the interest is compounded EACH YEAR

So, if the interest is compounded daily, then c = 365

Get it thanks Brent.

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