Find the compound interest on rs. 64,000 for 1 year at the rate of 10% per annum compounded quarterly (to the nearest integer).
Answers
compound interest = 6644 Rs
initial amount , P = 64,000
rate of interest per annum , r = 10%
time, n = 1 year = 4 quarters
now using formula, C.I = P(1 + r/400)ⁿ - P
= 64000(1 + 10/400)⁴ - 64000
= 64000(1 + 1/40)⁴ - 64000
here we have to apply Binomial expension of (1 + 1/40)⁴
(1 + 1/40)⁴ ≈ 1 + 4/40 + 4 × 3/2 × 40² + 4 × 3 × 2/6 × 40³
= 1 + 1/10 + 6/1600 + 4/64000
= 1 + 0.1 + 6/1600 + 1/16000
= 1 + 0.1 + 0.00375 + 0.0000625
= 1.1038125
then, C.I = 64000(1.1038125) - 64000
= 64000(1 + 0.1038125) - 64000
= 64000 × 0.1038125
= 6644
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The answer is ₹6644.03
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