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6.Interest
hard
If $Rs. 1200$ amounts to $Rs. 1323$ in $2$ years at compound interest compounded annually, what will $Rs. 1600$ amount (In $Rs.$) to in $3$ years at the same rate?
A
$1780.45$
B
$1852.50$
C
$1945.55$
D
$2166.76$
Solution
Here, Amount $= P \left[\left(1+\frac{ R }{100}\right)^{2}\right]$
$\Rightarrow 1323=1200\left[\left(1+\frac{ R }{100}\right)^{2}\right]$
$\Rightarrow \frac{1323}{1200}=\left(1+\frac{ R }{100}\right)^{2}$
On solving above equation we get Rate of interest $R =5 \%$
Hence, amount of principal = Rs. 1600 in 3 years would become:
$\Rightarrow A=1600\left[\left(1+\frac{5}{100}\right)^{3}\right]=1600\left[\frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}\right]$
$=\frac{1600}{8000}[21]^{3}=\frac{1}{5} \times 9261=$ Rs. 1852.50
Standard 13
Quantitative Aptitude
