Question

Find the difference between the simple interest and compound interest on $$Rs\ 4800$$ for $$2$$ years at $$5\%$$ per annum, compound interest being reckoned annually.

Solution

Simple Interest:$$P=Rs\ 4800$$                 $$r=5\% p.a$$                        $$t=2\ years$$$$\therefore SI=\dfrac{Ptr}{100}=Rs.\dfrac{4800\times 2\times 5}{100}=Rs\ 480$$Compound interest:Case I $$P=Rs\ 4800$$                 $$r=5\% p.a.$$                $$t=1\ year$$Interest $$=Rs.\dfrac{4800\times 5\times 1}{100}=Rs\ 240$$$$\therefore A=Rs\ (4800+240)=Rs\ 5040$$Case II $$P=Rs\ 5040$$           $$r=5\% p.a.$$                   $$t=1\ year$$Interest $$=Rs.\dfrac{5040\times 5\times 1}{100}=Rs\ 252.$$$$\therefore A=Rs\ (5040+252)=Rs\ 5292$$.$$\therefore$$ Compound Interest $$=Rs(5292-4800)=Rs\ 492$$$$\therefore$$ Difference between compound Interest and Simple Interest $$=Rs\ (492-480)=Rs.12$$          Mathematics

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