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unable to understand
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unable to understand


Can you specify where the difficulty lies?
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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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nityakaul02
unable to understand


Can you specify where the difficulty lies?

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

CrackVerbalGMAT
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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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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