Consider the compound interest in the following cases:
(A) The compound interest on Rs 16000 at 20%

Q: What is the correct answer for CUET UG Quantitative Aptitude?

The correct answer is B. Let's analyze each statement: (A) Compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly. Principal (P) = Rs 16000 Annual Rate (R) = 20% Time (T) = 9 months = $9/12 = 3/4$ year. Compounded quarterly, so number of compounding periods per year (n) = 4. Quarterly rate (r) = R/n = $20\%/4 = 5\% = 0.05$. Number of compounding periods (t) = T $\times$ n = $(3/4) \times 4 = 3$

Q: Consider the compound interest in the following cases: (A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500 (B) The compound interest on Rs 2800 at…

The correct answer is B. Let's analyze each statement: (A) Compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly. Principal (P) = Rs 16000 Annual Rate (R) = 20% Time (T) = 9 months = $9/12 = 3/4$ year. Compounded quarterly, so number of compounding periods per year (n) = 4. Quarterly rate (r) = R/n = $20\%/4 = 5\% = 0.05$. Number of compounding periods (t) = T $\times$ n = $(3/4) \times 4 = 3$

Q: What are the options for this CUET UG Quantitative Aptitude question?

A. Only (A) · B. Only (B) · C. and (B) · D. Neither (A) nor (B)

Question

Consider the compound interest in the following cases:
(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500
(B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434.
Choose the correct statment(s):

FirstInTest · Accepted Answer

Let's analyze each statement:

(A) Compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly.
Principal (P) = Rs 16000
Annual Rate (R) = 20%
Time (T) = 9 months = $9/12 = 3/4$ year.
Compounded quarterly, so number of compounding periods per year (n) = 4.
Quarterly rate (r) = R/n = $20\%/4 = 5\% = 0.05$.
Number of compounding periods (t) = T $	imes$ n = $(3/4) 	imes 4 = 3$.
Amount (A) = $P(1 + r)^t = 16000(1 + 0.05)^3 = 16000(1.05)^3$
$16000 	imes 1.157625 = 18522$.
Compound Interest (CI) = A - P = $18522 - 16000 = 2522$.
Statement (A) says CI is Rs. 2500. Since $2522 
e 2500$, statement (A) is Incorrect.

(B) Compound interest on Rs 2800 at 10% per annum for 18 months.
Principal (P) = Rs 2800
Annual Rate (R) = 10%
Time (T) = 18 months = $1.5$ years.
Since the compounding frequency is not specified, we assume it's compounded annually. For fractional years, we calculate the amount for the full year and then simple interest for the remaining fraction.
Amount after 1 year = $P(1 + R) = 2800(1 + 0.10) = 2800 	imes 1.1 = 3080$.
Interest for the remaining 0.5 year (6 months) on this amount at 10% simple interest:
Interest = $3080 	imes 0.10 	imes 0.5 = 308 	imes 0.5 = 154$.
Total Compound Interest = (Interest for 1st year) + (Interest for next 0.5 year)
Interest for 1st year = $2800 	imes 0.10 = 280$.
Total CI = $280 + 154 = 434$.
Statement (B) says CI is Rs. 434. Since $434 = 434$, statement (B) is Correct.

Therefore, only statement (B) is correct.

Answer

Only (A)

Answer

Only (B)

Answer

and (B)

Answer

Neither (A) nor (B)

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