The compound interest on a sum at 18 % p.a. for 1½ years, compounded yearly, is ₹2 862. Find the principal.
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Correct answer: A
Explanation
Given:
Compound interest = ₹2862
Rate = 18% per annum
Time = 1.5 years (compounded annually)
By the formula:
Amount = P(1 + R/100)ⁿ
Compound interest = Amount − Principal
Amount after 1 year = P(1 + 18/100) = 1.18P
Simple interest for the next 1/2 year = 1.18P × 18 × (1/2) / 100 = 0.1062P
Final amount = 1.18P + 0.1062P = 1.2862P
Compound interest = 1.2862P − P = 0.2862P
0.2862P = 2862
P = 2862 / 0.2862 = ₹10,000