Question
Calculate the rate per cent at which $Rs.16,000$ will yield $Rs.3,876.75$ as compound interest in $3$ years.
✓
Answer
$ P =\operatorname{Rs} 16,000 ; A =\operatorname{Rs}(16,000+3,876.75)= Rs.19,876.75 ; t =3 \text { years; } r =? $
$A = P \left(1+\frac{ r }{100}\right)^{ n } $
$ \text { Rs } 19,876.75=\operatorname{Rs} 16,000\left(1+\frac{ r }{100}\right)^3 $
$ \frac{19876.75}{16000}=\left(1+\frac{ r }{100}\right)^3$
$\frac{(27.08)^3}{(25.19)^3}=\left(1+\frac{ r }{100}\right)^3$
$ \frac{2708}{2519}=1+\frac{ r }{100}$
$ \frac{ r }{100}=\frac{2708}{2519}-1=\frac{2708-2519}{2519}=\frac{189}{2519} $
$ r =\frac{18900}{2519}=7.5 \%$
Hence, $r=7.5 \%$
$A = P \left(1+\frac{ r }{100}\right)^{ n } $
$ \text { Rs } 19,876.75=\operatorname{Rs} 16,000\left(1+\frac{ r }{100}\right)^3 $
$ \frac{19876.75}{16000}=\left(1+\frac{ r }{100}\right)^3$
$\frac{(27.08)^3}{(25.19)^3}=\left(1+\frac{ r }{100}\right)^3$
$ \frac{2708}{2519}=1+\frac{ r }{100}$
$ \frac{ r }{100}=\frac{2708}{2519}-1=\frac{2708-2519}{2519}=\frac{189}{2519} $
$ r =\frac{18900}{2519}=7.5 \%$
Hence, $r=7.5 \%$
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