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Question
Find the difference between Compound Interest and Simple Interest on Rs 45,000 at 12% per annum for 5 years.
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Solution
Principal (P) = ₹ 45000
Rate of interest (R) = 12% per annum
Time period (T) = 5 year
Simple interest, `SI = (P xx R xx T)/100`
= `(45000 xx 12 xx 5)/100`
= 450 × 60
= ₹ 27000
∵ Compound interest, CI = A – P
Where, `A = P(1 + R/100)^T`
`A = 45000(1 + 12/100)^5`
= `45000(28/25)^5`
= `45000 xx 28/25 xx 28/25 xx 28/25 xx 28/25 xx 28/25`
= `(45000 xx 17210368)/9765625`
= 45000 × 1.76
= ₹ 79200
∴ Compound interest, CI = ₹ 79200 – ₹ 45000 = ₹ 34200
∴ Difference between SI and CI = ₹ 34200 – ₹ 27000 = ₹ 7200
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