CA Foundation · Quantitative Aptitude · Mathematics of Finance
A sum is invested at 10% per annum compounded half-yearly. After 1 year it grows to ₹1,10,250. What was the sum invested, and what is the effective annual rate?
The sum invested was ₹1,00,000 and the effective rate is 10.25%. With a 5% half-yearly rate, the one-year growth factor is 1.05 squared, 1.1025. Dividing ₹1,10,250 by 1.1025 gives ₹1,00,000, and the factor shows 10.25% growth.
- A₹1,00,000; 10.25%Correct
- B₹1,00,000; 10%
- C₹1,05,000; 10.25%
- D₹99,000; 10.50%
Explanation
Half-yearly rate = 5%, so amount = P x (1.05)^2 = P x 1.1025. P = 1,10,250 / 1.1025 = 1,00,000. Effective rate = 1.1025 - 1 = 10.25%. Check: 1,00,000 x 1.1025 = 1,10,250.
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