A sum was divided into two equal parts. One part was lent at 20% p.a. simple interest. The other part was lent at 20% p.a. compound interest, interest being compounded annually. The difference in the interests fetched by the parts in the second year is Rs. 500. Find the difference in the interests fetched by the parts in the fourth year (in Rs.).
Explanation:
Let the total sum be 2P.
Interest accumulated when P was lent at 20% SI for 2 years = (P × 20 × 2)/100 = 2P/5 = 0.4P
Interest accumulated when P was lent at 20% CI for 2 years = 1.22P – P = 1.44P – P = 0.44P
∴ 0.44P – 0.4P = 500
⇒ P = 500/0.04 = 12,500
Interest accumulated when P was lent at 20% SI for 4th year = (P × 20 × 1)/100 = P/5 = 0.2P
Interest accumulated when P was lent at 20% CI for 4th year = P × 0.2 × 1.2 × 1.2 × 1.2 = 0.3456P
Difference in total interest for 4th year = 0.3456P – 0.2P = 0.1456P = 0.1456 × 12500 = 1820.
Hence, 1820.
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