Question

Marie bought a 1-year certificate of deposit and the annual interest earned on the deposit is 6 percent compounded semi-annually. What was the amount invested, if the interest earned on the certificate at maturity is 60.9?

• A. ₹ 100
• B. ₹ 1,000
• C. ₹ 1,010
• D. ₹ 1,100

Answer 1

The Correct Option is B

Step 1: Use the compound interest formula for semi-annual compounding: 

• A = P × (1 + r/n)^nt
• Where:
  • A is the final amount (principal + interest).
  • P is the principal.
  • r = 0.06 (annual interest rate).
  • n = 2 (number of compounding periods per year).
  • t = 1 (time in years).

Step 2: The interest earned is ₹60.9, so:

• A − P = 60.9 and A = P × (1 + 0.06/2)^2×1
• A = P × (1 + 0.03)² = P × 1.0609

Step 3: Now, solve for P:

• P × 1.0609 − P = 60.9
• P (1.0609 − 1) = 60.9 ⇒ P × 0.0609 = 60.9
• P = 60.9 ÷ 0.0609 = 1000

Conclusion: The amount invested is ₹1,000.