A sum becomes ₹6,600 in 2 years and ₹7,920 in 3 years at compound interest. What is the original principal?

A sum becomes ₹6,600 in 2 years and ₹7,920 in 3 years at compound interest. What is the original principal?

एक राशि चक्रवृद्धि ब्याज पर 2 वर्षों में ₹6,600 और 3 वर्षों में ₹7,920 हो जाती है। मूलधन ज्ञात कीजिए।

A. ₹4,000.33

B. ₹5,583.33

C. ₹4,583.33 ✅

D. ₹6,583.33

✅ ₹4,583.33

Under compound interest:

\frac{\text{Amount after 3 years}}{\text{Amount after 2 years}} = \frac{7920}{6600} = \frac{6}{5}

Thus, the annual growth factor is:

1+r=\frac{6}{5}

Since the amount after 2 years is ₹6600:

P\left(\frac{6}{5}\right)^2 = 6600

P \times \frac{36}{25} = 6600

P = 6600 \times \frac{25}{36}

P = 183.33 \times 25

P = 4583.33

Amount after 1 year:

6600 \times \frac{5}{6}=5500

Principal:

5500 \times \frac{5}{6} = 4583.33

\boxed{₹4,583.33}

✅ Correct Answer / सही उत्तर: ₹4,583.33

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