Simple Interest and Compound Interest

Question

The difference between the Simple Interest and compound interest (For the same principal and rate) after 2 years is $50.

If the same principal was kept for 3 years at Simple Interest, the interes accrued would be $480.

Find the rate% assuming that the principal and rate are the same for simple and compound interest.

A. 30.25%

B. 30.75%

C. 31.25%

D. 31.50%

E. 31.75%

globaldesi · Accepted Answer

that means 50 is the interest on S.I for 1 year
and simple interest for 3 years is 480 thus for 1 years =  \frac{480}{3}  = 160
or
 \frac{r*160}{100 } = 50
or r = 31.25
C IMO

MathRevolution · Answer

The difference between C.I. and S.I. for 2 years is given by  \frac{  }{ (100^2)}

=>  \frac{  }{ (100^2)}  = $50

=>  PR^2  = 50 * 100 * 100  --------Eqn(1)

S.I. for '3' years is $480

=> S.I. =  \frac{  }{ 100}

=> 480 =  \frac{  }{ 100}

=> P * R = 160 * 100 --------Eqn(2)

By  \frac{  }{  }

=>  \frac{  }{  }  =  \frac{  }{   }

=> R =  \frac{250}{8}

=> R = 31.25%

Answer C

nityakaul02 · Answer

unable to understand

CrackverbalGMAT · Answer

Can you specify where the difficulty lies?

gmexamtaker1 · Answer

Any help ?

so I got one equation from the Information given which is P*r*3=480 (160$/year)

also it says that the difference between S.I and C.I is Prt-  =50

after calculations I just got to a 160/r  =270 I didn't know how to proceed without knowing the times that it got compounded (n) , but even if I did know the "n", eventually I would come up against some "ugly" math .

nityakaul02 · Answer

the whole problem

CrackverbalGMAT · Answer

For the same principal and Rate of Interest

For t = 1, i.e the first year: SI = CI

For t = 2, i.e the second year: The difference between the SI and Compound interest, CI - SI =  P *\frac{r}{100} * \frac{r}{100}

So,  50 = P *\frac{r}{100} * \frac{r}{100}  ... (1)

SI for 3 years =  480 = P * \frac{r}{100} * 3

Therefore   P * \frac{r}{100} = \frac{480}{3} = 160

Putting this value in (1), we get

50 = 160 * \frac{r}{100}

r =  \frac{50 * 100}{160} = 31.25 %

Hope This helps

Arun Kumar

Ravs113 · Answer

Hi, Can you show the derivation part of CI-SI? How you reached to that formula.

Posted from my mobile device

CrackverbalGMAT · Answer

Hello Ravs113.

SI for 2 years =  \frac{2Pr}{100}

CI for 2 years =  P * (1 +\frac{r}{100})^2 - P = P(\frac{(100 + r)^2}{100^2} - P

CI - SI =  P\frac{(100^2 + 200r + r^2)}{100^2} - P - \frac{2Pr}{100}

Taking LCM as  100^2 , CI - SI =  \frac{P100^2 + 200Pr + Pr^2 - P100^2 - 200Pr}{100^2}

The first 2 terms and the last 2 terms cancel out, which gives us  \frac{Pr^2}{100^2} = P * \frac{r}{100} * \frac{r}{100}

Hope this helps

Arun

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Simple Interest and Compound Interest

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Simple Interest and Compound Interest

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards