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Find the compound interest on Rs 4000 when rate is 10 percent for first year and 7 percent for second year

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This Compound Interest problem develops accurate selection of the compounding formula for “Find the compound interest on Rs 4000 when rate is 10 percent for first year and 7 percent for second year” It requires candidates to identify the principal, nominal rate, number of periods and whether the target is amount, interest, rate, time or principal. The worked explanation preserves the question’s numerical data, verifies 558.0, and identifies common traps involving simple interest, premature rounding and incorrect period conversion. It is useful for SSC, Railway, Banking, State examinations and other quantitative-aptitude tests where speed must be supported by dependable calculation.

A558.0
B758.0
C858.0
D708.0
Correct Answer: 558.0Your Answer: A

Explanation

The calculation confirms 558.0 as the only matching option. Form the equation A/P = (1 + r/100)^n and solve for r. The supplied calculation is: A = P(1+R1/100)(1+R2/100), CI = 708.0. Compound interest differs from simple interest because each completed period adds interest to the balance, and the next period earns interest on that enlarged amount. The distractors 758.0, 858.0, 708.0 can arise from using simple interest, omitting the subtraction of principal, rounding too early, or applying the annual rate without adjusting the compounding frequency. A reliable verification is to rebuild the amount period by period and confirm that Amount − Principal equals the reported compound interest whenever interest, rather than amount, is requested. Also check reasonableness: with a positive rate the amount must exceed the principal, and more frequent compounding should not reduce the amount for the same nominal annual rate. This question strengthens formula selection, substitution accuracy and option elimination for SSC, Railway, banking and other aptitude examinations. The question-specific answer remains 558.0 after this independent check.

Important Notes

  • Correct answer: 558.0; option A, zero-based index
  • Method: Form the equation A/P = (1 + r/100)^n and solve for r.
  • Question-specific computation: A = P(1+R1/100)(1+R2/100), CI = 708.0
  • Keep rate and compounding period in compatible units before using the exponent.
  • Verify whether the question asks for amount or compound interest; CI = Amount − Principal.

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FAQ

Compound Interest FAQs

Common questions and clear answers for this topic.

Which formula applies to this question?

Form the equation A/P = (1 + r/100)^n and solve for r.

What is the verified answer?

558.0, option A.

What is the most common error in this calculation?

Using the wrong number of compounding periods or confusing amount with compound interest.

How can the result be checked?

Recalculate the accumulated amount period by period and compare it with the selected option.

What is Compound Interest and how is it different from Simple Interest?

Compound Interest (CI) is interest calculated on both the principal amount and the accumulated interest from previous periods. Simple Interest (SI) is calculated only on the principal. CI formula: A = P(1 + r/n)^(nt). CI gives more interest than SI for the same principal and rate. Both are important topics for SSC CGL, Bank PO, and CAT exams.

What is the formula for Compound Interest?

Compound Interest Formula: A = P(1 + R/100)^n where A = Final Amount, P = Principal, R = Annual Rate of Interest, n = Number of years. CI = A - P = P[(1 + R/100)^n - 1]. For half-yearly compounding: A = P(1 + R/200)^(2n). For quarterly: A = P(1 + R/400)^(4n). This formula is essential for SSC CGL and banking aptitude tests.

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