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Simple Interest and Compound Interest
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CrackVerbalGMAT
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Simple Interest and Compound Interest [#permalink] New post  01 Dec 2020, 19:26
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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%
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Re: Simple Interest and Compound Interest [#permalink] New post  01 Dec 2020, 19:44
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CrackVerbalGMAT wrote:
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%


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
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Simple Interest and Compound Interest [#permalink] New post  02 Dec 2020, 09:17
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The difference between C.I. and S.I. for 2 years is given by \(\frac{[PR^2] }{ (100^2)}\)

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

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

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

=> S.I. = \(\frac{[P * R * T] }{ 100}\)

=> 480 = \(\frac{[P * R * 3] }{ 100}\)

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

By \(\frac{[Eqn(1)] }{ [Eqn(2)]}\)

=> \(\frac{[PR^2] }{ [PR]}\) = \(\frac{[50 * 100 * 100] }{ [160 * 100] }\)

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

=> R = 31.25%

Answer C
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Re: Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 04:21
unable to understand
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Re: Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 04:44
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nityakaul02 wrote:
unable to understand



Can you specify where the difficulty lies?
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Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 06:02
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- [P(1+r/n)^nt - P]=50

after calculations I just got to a 160/r [(1+r/n)^n3 -1]=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 .
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Re: Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 07:38
CrackVerbalGMAT wrote:
nityakaul02 wrote:
unable to understand



Can you specify where the difficulty lies?


the whole problem
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Re: Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 18:17
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nityakaul02 wrote:
CrackVerbalGMAT wrote:
nityakaul02 wrote:
unable to understand



Can you specify where the difficulty lies?


the whole problem


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
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Re: Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 18:36
Hi, Can you show the derivation part of CI-SI? How you reached to that formula.

CrackVerbalGMAT wrote:
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


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Simple Interest and Compound Interest [#permalink] New post  12 Dec 2020, 19:50
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Ravs113 wrote:
Hi, Can you show the derivation part of CI-SI? How you reached to that formula.



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
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