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ICSE Class X Math 2013 Paper

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Question : 21 of 46
Marks: +1, -0
Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8%8\% per annum and Mr. Britto gets ₹8088\text{₹} 8088 from the bank after 3 years, find the value of his monthly instalment.
Solution:  
Let the monthly instalment be ₹x\text{₹} x
Given : M.V. =₹8,088=\text{₹} 8,088 , Time (n)=3(n)=3 years == 36 months, Rate (R)=8%(R)=8\% p.a.
I  =P×n(n+1)2×12×r100I\;= P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}
=x×36×372×12×8100= x \times \frac{36 \times 37}{2 \times 12} \times \frac{8}{100}
=444x100= \frac{444 x}{100}
Actual sum deposited    =36x\text{Actual sum deposited}\;\;=36 x
Maturity amount    =\text{Maturity amount}\;\;= Interest + Actual sum deposited
8,088  =  444x100+36x8,088\;=\;\frac{444 x}{100}+36 x
8,088  =  4,044x1008,088\;=\;\frac{4,044 x}{100}
∴    x  =  8,088×1004,044=200\therefore \; \; x\;=\;\frac{8,088 \times 100}{4,044}=200
Hence, the monthly instalment be ₹200\text{₹} 200.
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