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Question

A sum of money amounts to Rs. 46,305 in 1 year and to Rs. 48,620.25 in 112 years at compound interest, compounded semi-annually. Find the sum and the rate of interest per annum.

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Solution

Let the principle amount be Rs. x and rate be y% per annumFormula of amount in compound interest: A=P(1+rn)ntwhere A= AmountP=Principlen= number of times that interest is compounded per yeart= number of yearsr=rate(in decimals) per annumAmount after 1 year=Rs. 46305n=2−[since interest is compounded semi-annually]∴46305=P(1+y/1002)2×1 ......(1)Amount after 112year=Rs. 48620.2548620.25=P(1+y/1002)2×132 .......(2)Dividing equation (2) by (1), we get48620.2546305=(1+y200)On solving we get, y=10% p.a.Substituting the value of y in equation (1)∴46305=P(1+10/1002)2On solving the above equation, we getPrinciple(P)=Rs. 42,000.

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