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?
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?
Updated On: Mar 5, 2025
- ₹ 100
- ₹ 1,000
- ₹ 1,010
- ₹ 1,100
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The Correct Option is B
Solution and Explanation
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.
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