Question

Ex,4. The sum of money which when given on com- pound interest at 18% per annum would fetch Rs. 960 more when the interest is payable half yearly than when it was payable annually for 2 years is : (1) Rs.60,000 (2) Rs. 30,000 (3) Rs. 40,000 (4) Rs. 50,000

11th - 12th Class

Maths

Solution

131

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When the interest is payable half yearly, ( =9 % ) per half annum Time ( =4 ) half years Let the principal be Rs. P. ( therefore mathrm{C.I.}=mathrm{P}left[left(1+frac{mathrm{R}}{100}right)^{mathrm{T}}-1right] ) ( =mathrm{P}left[left(1+frac{9}{100}right)^{4}-1right]=mathrm{P}left[(1.09)^{4}-1right] ) ( =P[1.4116-1]=R s .0 .4116 P ) According to the question. ( =mathrm{P}left[left(1+frac{18}{100}right)^{2}-1right]=mathrm{P}left[(1.18)^{2}-1right] ) ( =P(1.3924-1)= ) Rs. ( 0.3924 P ) According to the question. ( 0.4116 P-0.3924 P=960 ) ( Rightarrow 0.0192 P=960 ) ( Rightarrow P=frac{960}{0.0192}=frac{960 times 10000}{192}= ) Rs. 50000