Question:
Daniel deposits ₹10000 in a fixed deposit earning \( p\% \) annual interest, compounded quarterly. What is the value of \( p \)?
Statement (I): He would have earned ₹18 less for the deposit period had he been paid simple interest.
Statement (II): He withdraws all the money six months after depositing it.
Daniel deposits ₹10000 in a fixed deposit earning \( p\% \) annual interest, compounded quarterly. What is the value of \( p \)?
Statement (I): He would have earned ₹18 less for the deposit period had he been paid simple interest.
Statement (II): He withdraws all the money six months after depositing it.
Statement (II): He withdraws all the money six months after depositing it.
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A relationship involving compound interest usually requires both the rate and the time period. If either is missing, the information is often insufficient.
Updated On: Jun 15, 2026
- Statement (I) alone is sufficient.
- Statement (II) alone is sufficient.
- Both statements (I) and (II) are sufficient.
- Neither statement is sufficient.
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The Correct Option is C
Solution and Explanation
Concept:
To determine the annual interest rate \(p\), we need enough information to form an equation containing only one unknown.
The principal amount is
\[
P = 10000
\]
and the interest is compounded quarterly.
Step 1: Analyze Statement (I) alone. Statement (I) tells us that \[ CI - SI = 18 \] Although this gives a relationship between compound interest and simple interest, the time period is unknown. Since the difference between CI and SI depends on both the rate \(p\) and the duration of investment, multiple values of \(p\) are possible. Therefore Statement (I) alone is insufficient.
Step 2: Analyze Statement (II) alone. Statement (II) tells us that the deposit remains invested for six months. This means \[ t=\frac12 \text{ year} \] or \[ 2 \text{ quarters} \] However, no information about the amount of interest earned is given. Therefore Statement (II) alone is insufficient.
Step 3: Combine Statements (I) and (II). From Statement (II), the investment lasts for two quarters. Thus \[ A=P\left(1+\frac{p}{400}\right)^2 \] and \[ SI=P\left(\frac{p}{100}\times \frac12\right) =10000\left(\frac{p}{200}\right) \] Using Statement (I), \[ CI-SI=18 \] Substituting the known values produces an equation containing only \(p\). Hence \(p\) can be uniquely determined. Therefore both statements together are sufficient. \[ \boxed{\text{Both statements (I) and (II) are sufficient}} \]
Step 1: Analyze Statement (I) alone. Statement (I) tells us that \[ CI - SI = 18 \] Although this gives a relationship between compound interest and simple interest, the time period is unknown. Since the difference between CI and SI depends on both the rate \(p\) and the duration of investment, multiple values of \(p\) are possible. Therefore Statement (I) alone is insufficient.
Step 2: Analyze Statement (II) alone. Statement (II) tells us that the deposit remains invested for six months. This means \[ t=\frac12 \text{ year} \] or \[ 2 \text{ quarters} \] However, no information about the amount of interest earned is given. Therefore Statement (II) alone is insufficient.
Step 3: Combine Statements (I) and (II). From Statement (II), the investment lasts for two quarters. Thus \[ A=P\left(1+\frac{p}{400}\right)^2 \] and \[ SI=P\left(\frac{p}{100}\times \frac12\right) =10000\left(\frac{p}{200}\right) \] Using Statement (I), \[ CI-SI=18 \] Substituting the known values produces an equation containing only \(p\). Hence \(p\) can be uniquely determined. Therefore both statements together are sufficient. \[ \boxed{\text{Both statements (I) and (II) are sufficient}} \]
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