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ICSE Class X Math 2014 Paper

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Question : 7 of 52
Marks: +1, -0
Shahrukh opened a Recurring Deposit Account in a bank and deposited 800\text{₹}\,800 per month for 1121\,\frac{1}{2} years. If he received 15,084\text{₹}\,15,084 at the time of maturity, find the rate of interest per annum.
Solution:  
Here, P=P= money deposited per month == ₹ 800
n=n= Time for which the money is deposited
=112years    =18months.=1\,\frac{1}{2}\,\text{years}_{\;\text{, }\;}=18\,\text{months.}\,
Let the rate of interest be r%r\% per annum, then
    Interest    =P×n(n+1)2×12×r100\therefore \;\; \text{Interest}\;\; = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}
=800×18×192×12×r100\,=800 \times \frac{18\times 19}{2\times 12} \times \frac{r}{100}
=114r\,=\text{₹}\,114\,r
Total money deposited =18×800=14,400=18 \times 800 = \text{₹}\,14,400
Since money deposited + interest == Maturity value
14,400+114r=15,08414,400+114\,r = 15,084
114r=15,08414,400114\,r = 15,084 - 14,400
114r=684114\,r = 684
r=684114=6r\,=\,\frac{684}{114}=6
Hence, rate of interest =6%=6\% p.a.
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